DSSTThirdBody.java
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package org.orekit.propagation.semianalytical.dsst.forces;
import org.hipparchus.CalculusFieldElement;
import org.hipparchus.Field;
import org.hipparchus.analysis.differentiation.FieldGradient;
import org.hipparchus.util.CombinatoricsUtils;
import org.hipparchus.util.FastMath;
import org.hipparchus.util.FieldSinCos;
import org.hipparchus.util.MathArrays;
import org.hipparchus.util.SinCos;
import org.orekit.attitudes.AttitudeProvider;
import org.orekit.bodies.CelestialBodies;
import org.orekit.bodies.CelestialBody;
import org.orekit.orbits.FieldOrbit;
import org.orekit.orbits.Orbit;
import org.orekit.propagation.FieldSpacecraftState;
import org.orekit.propagation.PropagationType;
import org.orekit.propagation.SpacecraftState;
import org.orekit.propagation.semianalytical.dsst.utilities.AuxiliaryElements;
import org.orekit.propagation.semianalytical.dsst.utilities.CjSjCoefficient;
import org.orekit.propagation.semianalytical.dsst.utilities.CoefficientsFactory;
import org.orekit.propagation.semianalytical.dsst.utilities.CoefficientsFactory.NSKey;
import org.orekit.propagation.semianalytical.dsst.utilities.FieldAuxiliaryElements;
import org.orekit.propagation.semianalytical.dsst.utilities.FieldCjSjCoefficient;
import org.orekit.propagation.semianalytical.dsst.utilities.FieldShortPeriodicsInterpolatedCoefficient;
import org.orekit.propagation.semianalytical.dsst.utilities.JacobiPolynomials;
import org.orekit.propagation.semianalytical.dsst.utilities.ShortPeriodicsInterpolatedCoefficient;
import org.orekit.propagation.semianalytical.dsst.utilities.hansen.FieldHansenThirdBodyLinear;
import org.orekit.propagation.semianalytical.dsst.utilities.hansen.HansenThirdBodyLinear;
import org.orekit.time.AbsoluteDate;
import org.orekit.time.FieldAbsoluteDate;
import org.orekit.utils.FieldTimeSpanMap;
import org.orekit.utils.ParameterDriver;
import org.orekit.utils.TimeSpanMap;
import java.lang.reflect.Array;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.Set;
import java.util.SortedMap;
/** Third body attraction perturbation to the
* {@link org.orekit.propagation.semianalytical.dsst.DSSTPropagator DSSTPropagator}.
*
* @author Romain Di Costanzo
* @author Pascal Parraud
* @author Bryan Cazabonne (field translation)
*/
public class DSSTThirdBody implements DSSTForceModel {
/** Name of the prefix for short period coefficients keys. */
public static final String SHORT_PERIOD_PREFIX = "DSST-3rd-body-";
/** Name of the single parameter of this model: the attraction coefficient. */
public static final String ATTRACTION_COEFFICIENT = " attraction coefficient";
/** Max power for summation. */
public static final int MAX_POWER = 22;
/** Truncation tolerance for big, eccentric orbits. */
public static final double BIG_TRUNCATION_TOLERANCE = 1.e-1;
/** Truncation tolerance for small orbits. */
public static final double SMALL_TRUNCATION_TOLERANCE = 1.9e-6;
/** Central attraction scaling factor.
* <p>
* We use a power of 2 to avoid numeric noise introduction
* in the multiplications/divisions sequences.
* </p>
*/
private static final double MU_SCALE = FastMath.scalb(1.0, 32);
/** Retrograde factor I.
* <p>
* DSST model needs equinoctial orbit as internal representation.
* Classical equinoctial elements have discontinuities when inclination
* is close to zero. In this representation, I = +1. <br>
* To avoid this discontinuity, another representation exists and equinoctial
* elements can be expressed in a different way, called "retrograde" orbit.
* This implies I = -1. <br>
* As Orekit doesn't implement the retrograde orbit, I is always set to +1.
* But for the sake of consistency with the theory, the retrograde factor
* has been kept in the formulas.
* </p>
*/
private static final int I = 1;
/** Number of points for interpolation. */
private static final int INTERPOLATION_POINTS = 3;
/** Maximum power for eccentricity used in short periodic computation. */
private static final int MAX_ECCPOWER_SP = 4;
/** V<sub>ns</sub> coefficients. */
private final SortedMap<NSKey, Double> Vns;
/** Force model static context. Initialized with short period terms. */
private DSSTThirdBodyStaticContext staticContext;
/** If false, the static context needs to be initialized. */
private boolean doesStaticContextNeedsInitialization;
/** The 3rd body to consider. */
private final CelestialBody body;
/** Short period terms. */
private ThirdBodyShortPeriodicCoefficients shortPeriods;
/** "Field" Short period terms. */
private Map<Field<?>, FieldThirdBodyShortPeriodicCoefficients<?>> fieldShortPeriods;
/** Drivers for third body attraction coefficient and gravitational parameter. */
private final List<ParameterDriver> parameterDrivers;
/** Hansen objects. */
private HansenObjects hansen;
/** Hansen objects for field elements. */
private Map<Field<?>, FieldHansenObjects<?>> fieldHansen;
/** Complete constructor.
* @param body the 3rd body to consider
* @param mu central attraction coefficient
* (<b>i.e., attraction coefficient of the central body, not the one of the 3rd body</b>)
* @see CelestialBodies
*/
public DSSTThirdBody(final CelestialBody body, final double mu) {
parameterDrivers = new ArrayList<>(2);
parameterDrivers.add(new ParameterDriver(body.getName() + DSSTThirdBody.ATTRACTION_COEFFICIENT,
body.getGM(), MU_SCALE,
0.0, Double.POSITIVE_INFINITY));
parameterDrivers.add(new ParameterDriver(DSSTNewtonianAttraction.CENTRAL_ATTRACTION_COEFFICIENT,
mu, MU_SCALE,
0.0, Double.POSITIVE_INFINITY));
this.body = body;
this.Vns = CoefficientsFactory.computeVns(MAX_POWER);
this.doesStaticContextNeedsInitialization = true;
fieldShortPeriods = new HashMap<>();
fieldHansen = new HashMap<>();
}
/** Get third body.
* @return third body
*/
public CelestialBody getBody() {
return body;
}
/** Initializes the static 3rd body context if needed.
* @param auxiliaryElements auxiliary elements
* @param x DSST Chi element
* @param r3 distance from center of mass of the central body to the 3rd body
* @param parameters force model parameters
*/
private void initializeStaticContextIfNeeded(final AuxiliaryElements auxiliaryElements,
final double x, final double r3,
final double[] parameters) {
if (doesStaticContextNeedsInitialization) {
staticContext = new DSSTThirdBodyStaticContext(auxiliaryElements, x, r3, parameters);
doesStaticContextNeedsInitialization = false;
}
}
/** Computes the highest power of the eccentricity and the highest power
* of a/R3 to appear in the truncated analytical power series expansion.
* <p>
* This method computes the upper value for the 3rd body potential and
* determines the maximal powers for the eccentricity and a/R3 producing
* potential terms bigger than a defined tolerance.
* </p>
* @param auxiliaryElements auxiliary elements related to the current orbit
* @param type type of the elements used during the propagation
* @param parameters values of the force model parameters for state date (1 value for each parameters)
*/
@Override
public List<ShortPeriodTerms> initializeShortPeriodTerms(final AuxiliaryElements auxiliaryElements,
final PropagationType type,
final double[] parameters) {
// Initializes specific parameters.
final DSSTThirdBodyDynamicContext context = initializeStep(auxiliaryElements, parameters);
// Static context
initializeStaticContextIfNeeded(auxiliaryElements, context.getX(), context.getR3(), parameters);
// Hansen objects
hansen = new HansenObjects();
// Initialize short period terms
final int jMax = staticContext.getMaxAR3Pow() + 1;
shortPeriods = new ThirdBodyShortPeriodicCoefficients(jMax, INTERPOLATION_POINTS,
staticContext.getMaxFreqF(), body.getName(),
new TimeSpanMap<>(new Slot(jMax, INTERPOLATION_POINTS)));
final List<ShortPeriodTerms> list = new ArrayList<>();
list.add(shortPeriods);
return list;
}
/** {@inheritDoc} */
@Override
public <T extends CalculusFieldElement<T>> List<FieldShortPeriodTerms<T>> initializeShortPeriodTerms(final FieldAuxiliaryElements<T> auxiliaryElements,
final PropagationType type,
final T[] parameters) {
// Field used by default
final Field<T> field = auxiliaryElements.getDate().getField();
// Initializes specific parameters.
final FieldDSSTThirdBodyDynamicContext<T> context = initializeStep(auxiliaryElements, parameters);
// Static context (only provide integers. So, derivatives are not taken into account and getReal() method is accepted)
initializeStaticContextIfNeeded(auxiliaryElements.toAuxiliaryElements(), context.getX().getReal(), context.getR3().getReal(), getParameters());
// Hansen object
fieldHansen.put(field, new FieldHansenObjects<>(field));
// Initialize short period terms
final int jMax = staticContext.getMaxAR3Pow() + 1;
final FieldThirdBodyShortPeriodicCoefficients<T> ftbspc =
new FieldThirdBodyShortPeriodicCoefficients<>(jMax, INTERPOLATION_POINTS,
staticContext.getMaxFreqF(), body.getName(),
new FieldTimeSpanMap<>(new FieldSlot<>(jMax,
INTERPOLATION_POINTS),
field));
fieldShortPeriods.put(field, ftbspc);
return Collections.singletonList(ftbspc);
}
/** Performs initialization at each integration step for the current force model.
* <p>
* This method aims at being called before mean elements rates computation.
* </p>
* @param auxiliaryElements auxiliary elements related to the current orbit
* @param parameters values of the force model parameters (only 1 values for each parameters corresponding
* to state date) obtained by calling the extract parameter method {@link #extractParameters(double[], AbsoluteDate)}
* to selected the right value for state date or by getting the parameters for a specific date
* {@link #getParameters(AbsoluteDate)}.
* @return new force model context
*/
private DSSTThirdBodyDynamicContext initializeStep(final AuxiliaryElements auxiliaryElements, final double[] parameters) {
return new DSSTThirdBodyDynamicContext(auxiliaryElements, body, parameters);
}
/** Performs initialization at each integration step for the current force model.
* <p>
* This method aims at being called before mean elements rates computation.
* </p>
* @param <T> type of the elements
* @param auxiliaryElements auxiliary elements related to the current orbit
* @param parameters values of the force model parameters at state date (1 value per parameter driver)
* @return new force model context
*/
private <T extends CalculusFieldElement<T>> FieldDSSTThirdBodyDynamicContext<T> initializeStep(final FieldAuxiliaryElements<T> auxiliaryElements,
final T[] parameters) {
return new FieldDSSTThirdBodyDynamicContext<>(auxiliaryElements, body, parameters);
}
/** {@inheritDoc} */
@Override
public double[] getMeanElementRate(final SpacecraftState currentState,
final AuxiliaryElements auxiliaryElements, final double[] parameters) {
// Container for attributes
final DSSTThirdBodyDynamicContext context = initializeStep(auxiliaryElements, parameters);
// a / R3 up to power maxAR3Pow
final double[] aoR3Pow = computeAoR3Pow(context);
// Qns coefficients
final double[][] Qns = CoefficientsFactory.computeQns(context.getGamma(), staticContext.getMaxAR3Pow(), FastMath.max(staticContext.getMaxEccPow(), MAX_ECCPOWER_SP));
// Access to potential U derivatives
final UAnddU udu = new UAnddU(context, hansen, aoR3Pow, Qns);
// Compute cross derivatives [Eq. 2.2-(8)]
// U(alpha,gamma) = alpha * dU/dgamma - gamma * dU/dalpha
final double UAlphaGamma = context.getAlpha() * udu.getdUdGa() - context.getGamma() * udu.getdUdAl();
// U(beta,gamma) = beta * dU/dgamma - gamma * dU/dbeta
final double UBetaGamma = context.getBeta() * udu.getdUdGa() - context.getGamma() * udu.getdUdBe();
// Common factor
final double pUAGmIqUBGoAB = (auxiliaryElements.getP() * UAlphaGamma - I * auxiliaryElements.getQ() * UBetaGamma) * context.getOoAB();
// Compute mean elements rates [Eq. 3.1-(1)]
final double da = 0.;
final double dh = context.getBoA() * udu.getdUdk() + auxiliaryElements.getK() * pUAGmIqUBGoAB;
final double dk = -context.getBoA() * udu.getdUdh() - auxiliaryElements.getH() * pUAGmIqUBGoAB;
final double dp = context.getMCo2AB() * UBetaGamma;
final double dq = context.getMCo2AB() * UAlphaGamma * I;
final double dM = context.getM2aoA() * udu.getdUda() + context.getBoABpo() * (auxiliaryElements.getH() * udu.getdUdh() + auxiliaryElements.getK() * udu.getdUdk()) + pUAGmIqUBGoAB;
return new double[] {da, dk, dh, dq, dp, dM};
}
/** {@inheritDoc} */
@Override
public <T extends CalculusFieldElement<T>> T[] getMeanElementRate(final FieldSpacecraftState<T> currentState,
final FieldAuxiliaryElements<T> auxiliaryElements,
final T[] parameters) {
// Parameters for array building
final Field<T> field = currentState.getDate().getField();
final T zero = field.getZero();
// Container for attributes
final FieldDSSTThirdBodyDynamicContext<T> context = initializeStep(auxiliaryElements, parameters);
// a / R3 up to power maxAR3Pow
final T[] aoR3Pow = computeAoR3Pow(context);
// Qns coefficients
final T[][] Qns = CoefficientsFactory.computeQns(context.getGamma(), staticContext.getMaxAR3Pow(), FastMath.max(staticContext.getMaxEccPow(), MAX_ECCPOWER_SP));
// Hansen objects
@SuppressWarnings("unchecked")
final FieldHansenObjects<T> fho = (FieldHansenObjects<T>) fieldHansen.get(field);
// Access to potential U derivatives
final FieldUAnddU<T> udu = new FieldUAnddU<>(context, fho, aoR3Pow, Qns);
// Compute cross derivatives [Eq. 2.2-(8)]
// U(alpha,gamma) = alpha * dU/dgamma - gamma * dU/dalpha
final T UAlphaGamma = udu.getdUdGa().multiply(context.getAlpha()).subtract(udu.getdUdAl().multiply(context.getGamma()));
// U(beta,gamma) = beta * dU/dgamma - gamma * dU/dbeta
final T UBetaGamma = udu.getdUdGa().multiply(context.getBeta()).subtract(udu.getdUdBe().multiply(context.getGamma()));
// Common factor
final T pUAGmIqUBGoAB = (UAlphaGamma.multiply(auxiliaryElements.getP()).subtract(UBetaGamma.multiply(auxiliaryElements.getQ()).multiply(I))).multiply(context.getOoAB());
// Compute mean elements rates [Eq. 3.1-(1)]
final T da = zero;
final T dh = udu.getdUdk().multiply(context.getBoA()).add(pUAGmIqUBGoAB.multiply(auxiliaryElements.getK()));
final T dk = ((udu.getdUdh().multiply(context.getBoA())).negate()).subtract(pUAGmIqUBGoAB.multiply(auxiliaryElements.getH()));
final T dp = UBetaGamma.multiply(context.getMCo2AB());
final T dq = UAlphaGamma.multiply(I).multiply(context.getMCo2AB());
final T dM = pUAGmIqUBGoAB.add(udu.getdUda().multiply(context.getM2aoA())).add((udu.getdUdh().multiply(auxiliaryElements.getH()).add(udu.getdUdk().multiply(auxiliaryElements.getK()))).multiply(context.getBoABpo()));
final T[] elements = MathArrays.buildArray(field, 6);
elements[0] = da;
elements[1] = dk;
elements[2] = dh;
elements[3] = dq;
elements[4] = dp;
elements[5] = dM;
return elements;
}
/** {@inheritDoc} */
@Override
public void updateShortPeriodTerms(final double[] parameters, final SpacecraftState... meanStates) {
final Slot slot = shortPeriods.createSlot(meanStates);
for (final SpacecraftState meanState : meanStates) {
// Auxiliary elements related to the current orbit
final AuxiliaryElements auxiliaryElements = new AuxiliaryElements(meanState.getOrbit(), I);
// Extract the proper parameters valid for the corresponding meanState date from the input array
final double[] extractedParameters = this.extractParameters(parameters, auxiliaryElements.getDate());
// Container of attributes
final DSSTThirdBodyDynamicContext context = initializeStep(auxiliaryElements, extractedParameters);
// a / R3 up to power maxAR3Pow
final double[] aoR3Pow = computeAoR3Pow(context);
// Qns coefficients
final double[][] Qns = CoefficientsFactory.computeQns(context.getGamma(), staticContext.getMaxAR3Pow(), FastMath.max(staticContext.getMaxEccPow(), MAX_ECCPOWER_SP));
final GeneratingFunctionCoefficients gfCoefs =
new GeneratingFunctionCoefficients(staticContext.getMaxAR3Pow(), MAX_ECCPOWER_SP, staticContext.getMaxAR3Pow() + 1, context, hansen, aoR3Pow, Qns);
//Compute additional quantities
// 2 * a / An
final double ax2oAn = -context.getM2aoA() / context.getMeanMotion();
// B / An
final double BoAn = context.getBoA() / context.getMeanMotion();
// 1 / ABn
final double ooABn = context.getOoAB() / context.getMeanMotion();
// C / 2ABn
final double Co2ABn = -context.getMCo2AB() / context.getMeanMotion();
// B / (A * (1 + B) * n)
final double BoABpon = context.getBoABpo() / context.getMeanMotion();
// -3 / n²a² = -3 / nA
final double m3onA = -3 / (context.getA() * context.getMeanMotion());
//Compute the C<sub>i</sub><sup>j</sup> and S<sub>i</sub><sup>j</sup> coefficients.
for (int j = 1; j < slot.cij.length; j++) {
// First compute the C<sub>i</sub><sup>j</sup> coefficients
final double[] currentCij = new double[6];
// Compute the cross derivatives operator :
final double SAlphaGammaCj = context.getAlpha() * gfCoefs.getdSdgammaCj(j) - context.getGamma() * gfCoefs.getdSdalphaCj(j);
final double SAlphaBetaCj = context.getAlpha() * gfCoefs.getdSdbetaCj(j) - context.getBeta() * gfCoefs.getdSdalphaCj(j);
final double SBetaGammaCj = context.getBeta() * gfCoefs.getdSdgammaCj(j) - context.getGamma() * gfCoefs.getdSdbetaCj(j);
final double ShkCj = auxiliaryElements.getH() * gfCoefs.getdSdkCj(j) - auxiliaryElements.getK() * gfCoefs.getdSdhCj(j);
final double pSagmIqSbgoABnCj = (auxiliaryElements.getP() * SAlphaGammaCj - I * auxiliaryElements.getQ() * SBetaGammaCj) * ooABn;
final double ShkmSabmdSdlCj = ShkCj - SAlphaBetaCj - gfCoefs.getdSdlambdaCj(j);
currentCij[0] = ax2oAn * gfCoefs.getdSdlambdaCj(j);
currentCij[1] = -(BoAn * gfCoefs.getdSdhCj(j) + auxiliaryElements.getH() * pSagmIqSbgoABnCj + auxiliaryElements.getK() * BoABpon * gfCoefs.getdSdlambdaCj(j));
currentCij[2] = BoAn * gfCoefs.getdSdkCj(j) + auxiliaryElements.getK() * pSagmIqSbgoABnCj - auxiliaryElements.getH() * BoABpon * gfCoefs.getdSdlambdaCj(j);
currentCij[3] = Co2ABn * (auxiliaryElements.getQ() * ShkmSabmdSdlCj - I * SAlphaGammaCj);
currentCij[4] = Co2ABn * (auxiliaryElements.getP() * ShkmSabmdSdlCj - SBetaGammaCj);
currentCij[5] = -ax2oAn * gfCoefs.getdSdaCj(j) + BoABpon * (auxiliaryElements.getH() * gfCoefs.getdSdhCj(j) + auxiliaryElements.getK() * gfCoefs.getdSdkCj(j)) + pSagmIqSbgoABnCj + m3onA * gfCoefs.getSCj(j);
// add the computed coefficients to the interpolators
slot.cij[j].addGridPoint(meanState.getDate(), currentCij);
// Compute the S<sub>i</sub><sup>j</sup> coefficients
final double[] currentSij = new double[6];
// Compute the cross derivatives operator :
final double SAlphaGammaSj = context.getAlpha() * gfCoefs.getdSdgammaSj(j) - context.getGamma() * gfCoefs.getdSdalphaSj(j);
final double SAlphaBetaSj = context.getAlpha() * gfCoefs.getdSdbetaSj(j) - context.getBeta() * gfCoefs.getdSdalphaSj(j);
final double SBetaGammaSj = context.getBeta() * gfCoefs.getdSdgammaSj(j) - context.getGamma() * gfCoefs.getdSdbetaSj(j);
final double ShkSj = auxiliaryElements.getH() * gfCoefs.getdSdkSj(j) - auxiliaryElements.getK() * gfCoefs.getdSdhSj(j);
final double pSagmIqSbgoABnSj = (auxiliaryElements.getP() * SAlphaGammaSj - I * auxiliaryElements.getQ() * SBetaGammaSj) * ooABn;
final double ShkmSabmdSdlSj = ShkSj - SAlphaBetaSj - gfCoefs.getdSdlambdaSj(j);
currentSij[0] = ax2oAn * gfCoefs.getdSdlambdaSj(j);
currentSij[1] = -(BoAn * gfCoefs.getdSdhSj(j) + auxiliaryElements.getH() * pSagmIqSbgoABnSj + auxiliaryElements.getK() * BoABpon * gfCoefs.getdSdlambdaSj(j));
currentSij[2] = BoAn * gfCoefs.getdSdkSj(j) + auxiliaryElements.getK() * pSagmIqSbgoABnSj - auxiliaryElements.getH() * BoABpon * gfCoefs.getdSdlambdaSj(j);
currentSij[3] = Co2ABn * (auxiliaryElements.getQ() * ShkmSabmdSdlSj - I * SAlphaGammaSj);
currentSij[4] = Co2ABn * (auxiliaryElements.getP() * ShkmSabmdSdlSj - SBetaGammaSj);
currentSij[5] = -ax2oAn * gfCoefs.getdSdaSj(j) + BoABpon * (auxiliaryElements.getH() * gfCoefs.getdSdhSj(j) + auxiliaryElements.getK() * gfCoefs.getdSdkSj(j)) + pSagmIqSbgoABnSj + m3onA * gfCoefs.getSSj(j);
// add the computed coefficients to the interpolators
slot.sij[j].addGridPoint(meanState.getDate(), currentSij);
if (j == 1) {
//Compute the C⁰ coefficients using Danielson 2.5.2-15a.
final double[] value = new double[6];
for (int i = 0; i < 6; ++i) {
value[i] = currentCij[i] * auxiliaryElements.getK() / 2. + currentSij[i] * auxiliaryElements.getH() / 2.;
}
slot.cij[0].addGridPoint(meanState.getDate(), value);
}
}
}
}
/** {@inheritDoc} */
@Override
@SuppressWarnings("unchecked")
public <T extends CalculusFieldElement<T>> void updateShortPeriodTerms(final T[] parameters,
final FieldSpacecraftState<T>... meanStates) {
// Field used by default
final Field<T> field = meanStates[0].getDate().getField();
final FieldThirdBodyShortPeriodicCoefficients<T> ftbspc = (FieldThirdBodyShortPeriodicCoefficients<T>) fieldShortPeriods.get(field);
final FieldSlot<T> slot = ftbspc.createSlot(meanStates);
for (final FieldSpacecraftState<T> meanState : meanStates) {
// Auxiliary elements related to the current orbit
final FieldAuxiliaryElements<T> auxiliaryElements = new FieldAuxiliaryElements<>(meanState.getOrbit(), I);
// Extract the proper parameters valid for the corresponding meanState date from the input array
final T[] extractedParameters = this.extractParameters(parameters, auxiliaryElements.getDate());
// Container of attributes
final FieldDSSTThirdBodyDynamicContext<T> context = initializeStep(auxiliaryElements, extractedParameters);
// a / R3 up to power maxAR3Pow
final T[] aoR3Pow = computeAoR3Pow(context);
// Qns coefficients
final T[][] Qns = CoefficientsFactory.computeQns(context.getGamma(), staticContext.getMaxAR3Pow(), FastMath.max(staticContext.getMaxEccPow(), MAX_ECCPOWER_SP));
final FieldGeneratingFunctionCoefficients<T> gfCoefs =
new FieldGeneratingFunctionCoefficients<>(staticContext.getMaxAR3Pow(), MAX_ECCPOWER_SP, staticContext.getMaxAR3Pow() + 1,
context, (FieldHansenObjects<T>) fieldHansen.get(field), field, aoR3Pow, Qns);
//Compute additional quantities
// 2 * a / An
final T ax2oAn = context.getM2aoA().negate().divide(context.getMeanMotion());
// B / An
final T BoAn = context.getBoA().divide(context.getMeanMotion());
// 1 / ABn
final T ooABn = context.getOoAB().divide(context.getMeanMotion());
// C / 2ABn
final T Co2ABn = context.getMCo2AB().negate().divide(context.getMeanMotion());
// B / (A * (1 + B) * n)
final T BoABpon = context.getBoABpo().divide(context.getMeanMotion());
// -3 / n²a² = -3 / nA
final T m3onA = context.getA().multiply(context.getMeanMotion()).divide(-3.).reciprocal();
//Compute the C<sub>i</sub><sup>j</sup> and S<sub>i</sub><sup>j</sup> coefficients.
for (int j = 1; j < slot.cij.length; j++) {
// First compute the C<sub>i</sub><sup>j</sup> coefficients
final T[] currentCij = MathArrays.buildArray(field, 6);
// Compute the cross derivatives operator :
final T SAlphaGammaCj = context.getAlpha().multiply(gfCoefs.getdSdgammaCj(j)).subtract(context.getGamma().multiply(gfCoefs.getdSdalphaCj(j)));
final T SAlphaBetaCj = context.getAlpha().multiply(gfCoefs.getdSdbetaCj(j)).subtract(context.getBeta().multiply(gfCoefs.getdSdalphaCj(j)));
final T SBetaGammaCj = context.getBeta().multiply(gfCoefs.getdSdgammaCj(j)).subtract(context.getGamma().multiply(gfCoefs.getdSdbetaCj(j)));
final T ShkCj = auxiliaryElements.getH().multiply(gfCoefs.getdSdkCj(j)).subtract(auxiliaryElements.getK().multiply(gfCoefs.getdSdhCj(j)));
final T pSagmIqSbgoABnCj = ooABn.multiply(auxiliaryElements.getP().multiply(SAlphaGammaCj).subtract(auxiliaryElements.getQ().multiply(SBetaGammaCj).multiply(I)));
final T ShkmSabmdSdlCj = ShkCj.subtract(SAlphaBetaCj).subtract(gfCoefs.getdSdlambdaCj(j));
currentCij[0] = ax2oAn.multiply(gfCoefs.getdSdlambdaCj(j));
currentCij[1] = BoAn.multiply(gfCoefs.getdSdhCj(j)).add(auxiliaryElements.getH().multiply(pSagmIqSbgoABnCj)).add(auxiliaryElements.getK().multiply(BoABpon).multiply(gfCoefs.getdSdlambdaCj(j))).negate();
currentCij[2] = BoAn.multiply(gfCoefs.getdSdkCj(j)).add(auxiliaryElements.getK().multiply(pSagmIqSbgoABnCj)).subtract(auxiliaryElements.getH().multiply(BoABpon).multiply(gfCoefs.getdSdlambdaCj(j)));
currentCij[3] = Co2ABn.multiply(auxiliaryElements.getQ().multiply(ShkmSabmdSdlCj).subtract(SAlphaGammaCj.multiply(I)));
currentCij[4] = Co2ABn.multiply(auxiliaryElements.getP().multiply(ShkmSabmdSdlCj).subtract(SBetaGammaCj));
currentCij[5] = ax2oAn.negate().multiply(gfCoefs.getdSdaCj(j)).add(BoABpon.multiply(auxiliaryElements.getH().multiply(gfCoefs.getdSdhCj(j)).add(auxiliaryElements.getK().multiply(gfCoefs.getdSdkCj(j))))).add(pSagmIqSbgoABnCj).add(m3onA.multiply(gfCoefs.getSCj(j)));
// add the computed coefficients to the interpolators
slot.cij[j].addGridPoint(meanState.getDate(), currentCij);
// Compute the S<sub>i</sub><sup>j</sup> coefficients
final T[] currentSij = MathArrays.buildArray(field, 6);
// Compute the cross derivatives operator :
final T SAlphaGammaSj = context.getAlpha().multiply(gfCoefs.getdSdgammaSj(j)).subtract(context.getGamma().multiply(gfCoefs.getdSdalphaSj(j)));
final T SAlphaBetaSj = context.getAlpha().multiply(gfCoefs.getdSdbetaSj(j)).subtract(context.getBeta().multiply(gfCoefs.getdSdalphaSj(j)));
final T SBetaGammaSj = context.getBeta().multiply(gfCoefs.getdSdgammaSj(j)).subtract(context.getGamma().multiply(gfCoefs.getdSdbetaSj(j)));
final T ShkSj = auxiliaryElements.getH().multiply(gfCoefs.getdSdkSj(j)).subtract(auxiliaryElements.getK().multiply(gfCoefs.getdSdhSj(j)));
final T pSagmIqSbgoABnSj = ooABn.multiply(auxiliaryElements.getP().multiply(SAlphaGammaSj).subtract(auxiliaryElements.getQ().multiply(SBetaGammaSj).multiply(I)));
final T ShkmSabmdSdlSj = ShkSj.subtract(SAlphaBetaSj).subtract(gfCoefs.getdSdlambdaSj(j));
currentSij[0] = ax2oAn.multiply(gfCoefs.getdSdlambdaSj(j));
currentSij[1] = BoAn.multiply(gfCoefs.getdSdhSj(j)).add(auxiliaryElements.getH().multiply(pSagmIqSbgoABnSj)).add(auxiliaryElements.getK().multiply(BoABpon).multiply(gfCoefs.getdSdlambdaSj(j))).negate();
currentSij[2] = BoAn.multiply(gfCoefs.getdSdkSj(j)).add(auxiliaryElements.getK().multiply(pSagmIqSbgoABnSj)).subtract(auxiliaryElements.getH().multiply(BoABpon).multiply(gfCoefs.getdSdlambdaSj(j)));
currentSij[3] = Co2ABn.multiply(auxiliaryElements.getQ().multiply(ShkmSabmdSdlSj).subtract(SAlphaGammaSj.multiply(I)));
currentSij[4] = Co2ABn.multiply(auxiliaryElements.getP().multiply(ShkmSabmdSdlSj).subtract(SBetaGammaSj));
currentSij[5] = ax2oAn.negate().multiply(gfCoefs.getdSdaSj(j)).add(BoABpon.multiply(auxiliaryElements.getH().multiply(gfCoefs.getdSdhSj(j)).add(auxiliaryElements.getK().multiply(gfCoefs.getdSdkSj(j))))).add(pSagmIqSbgoABnSj).add(m3onA.multiply(gfCoefs.getSSj(j)));
// add the computed coefficients to the interpolators
slot.sij[j].addGridPoint(meanState.getDate(), currentSij);
if (j == 1) {
//Compute the C⁰ coefficients using Danielson 2.5.2-15a.
final T[] value = MathArrays.buildArray(field, 6);
for (int i = 0; i < 6; ++i) {
value[i] = currentCij[i].multiply(auxiliaryElements.getK()).divide(2.).add(currentSij[i].multiply(auxiliaryElements.getH()).divide(2.));
}
slot.cij[0].addGridPoint(meanState.getDate(), value);
}
}
}
}
/**
* Computes a / R3 to the power maxAR3Pow.
* @param context force model dynamic context
* @return aoR3Pow array
*/
private double[] computeAoR3Pow(final DSSTThirdBodyDynamicContext context) {
// a / R3 up to power maxAR3Pow
final double aoR3 = context.getAuxiliaryElements().getSma() / context.getR3();
final double[] aoR3Pow = new double[staticContext.getMaxAR3Pow() + 1];
aoR3Pow[0] = 1.;
for (int i = 1; i <= staticContext.getMaxAR3Pow(); i++) {
aoR3Pow[i] = aoR3 * aoR3Pow[i - 1];
}
return aoR3Pow;
}
/**
* Computes a / R3 to the power maxAR3Pow.
* @param context force model dynamic context
* @param <T> type of the elements
* @return aoR3Pow array
*/
private <T extends CalculusFieldElement<T>> T[] computeAoR3Pow(final FieldDSSTThirdBodyDynamicContext<T> context) {
final Field<T> field = context.getA().getField();
// a / R3 up to power maxAR3Pow
final T aoR3 = context.getFieldAuxiliaryElements().getSma().divide(context.getR3());
final T[] aoR3Pow = MathArrays.buildArray(field, staticContext.getMaxAR3Pow() + 1);
aoR3Pow[0] = field.getOne();
for (int i = 1; i <= staticContext.getMaxAR3Pow(); i++) {
aoR3Pow[i] = aoR3.multiply(aoR3Pow[i - 1]);
}
return aoR3Pow;
}
/** {@inheritDoc} */
@Override
public void registerAttitudeProvider(final AttitudeProvider provider) {
//nothing is done since this contribution is not sensitive to attitude
}
/** {@inheritDoc} */
@Override
public List<ParameterDriver> getParametersDrivers() {
return Collections.unmodifiableList(parameterDrivers);
}
/** Computes the C<sup>j</sup> and S<sup>j</sup> coefficients Danielson 4.2-(15,16)
* and their derivatives.
* <p>
* CS Mathematical Report $3.5.3.2
* </p>
*/
private class FourierCjSjCoefficients {
/** The coefficients G<sub>n, s</sub> and their derivatives. */
private final GnsCoefficients gns;
/** the coefficients e<sup>-|j-s|</sup>*w<sub>j</sub><sup>n, s</sup> and their derivatives by h and k. */
private final WnsjEtomjmsCoefficient wnsjEtomjmsCoefficient;
/** The terms containing the coefficients C<sub>j</sub> and S<sub>j</sub> of (α, β) or (k, h). */
private final CjSjAlphaBetaKH ABDECoefficients;
/** The Fourier coefficients C<sup>j</sup> and their derivatives.
* <p>
* Each column of the matrix contains the following values: <br/>
* - C<sup>j</sup> <br/>
* - dC<sup>j</sup> / da <br/>
* - dC<sup>j</sup> / dk <br/>
* - dC<sup>j</sup> / dh <br/>
* - dC<sup>j</sup> / dα <br/>
* - dC<sup>j</sup> / dβ <br/>
* - dC<sup>j</sup> / dγ <br/>
* </p>
*/
private final double[][] cj;
/** The S<sup>j</sup> coefficients and their derivatives.
* <p>
* Each column of the matrix contains the following values: <br/>
* - S<sup>j</sup> <br/>
* - dS<sup>j</sup> / da <br/>
* - dS<sup>j</sup> / dk <br/>
* - dS<sup>j</sup> / dh <br/>
* - dS<sup>j</sup> / dα <br/>
* - dS<sup>j</sup> / dβ <br/>
* - dS<sup>j</sup> / dγ <br/>
* </p>
*/
private final double[][] sj;
/** The Coefficients C<sup>j</sup><sub>,λ</sub>.
* <p>
* See Danielson 4.2-21
* </p>
*/
private final double[] cjlambda;
/** The Coefficients S<sup>j</sup><sub>,λ</sub>.
* <p>
* See Danielson 4.2-21
* </p>
*/
private final double[] sjlambda;
/** Maximum value for n. */
private final int nMax;
/** Maximum value for s. */
private final int sMax;
/** Maximum value for j. */
private final int jMax;
/**
* Private constructor.
*
* @param nMax maximum value for n index
* @param sMax maximum value for s index
* @param jMax maximum value for j index
* @param context container for dynamic force model attributes
* @param aoR3Pow a / R3 up to power maxAR3Pow
* @param qns Qns coefficients
*/
FourierCjSjCoefficients(final int nMax, final int sMax, final int jMax,
final DSSTThirdBodyDynamicContext context,
final double[] aoR3Pow, final double[][] qns) {
//Save parameters
this.nMax = nMax;
this.sMax = sMax;
this.jMax = jMax;
//Create objects
wnsjEtomjmsCoefficient = new WnsjEtomjmsCoefficient(context);
ABDECoefficients = new CjSjAlphaBetaKH(context);
gns = new GnsCoefficients(nMax, sMax, context, aoR3Pow, qns);
//create arays
this.cj = new double[7][jMax + 1];
this.sj = new double[7][jMax + 1];
this.cjlambda = new double[jMax];
this.sjlambda = new double[jMax];
computeCoefficients(context);
}
/**
* Compute all coefficients.
* @param context container for attributes
*/
private void computeCoefficients(final DSSTThirdBodyDynamicContext context) {
final AuxiliaryElements auxiliaryElements = context.getAuxiliaryElements();
for (int j = 1; j <= jMax; j++) {
// initialise the coefficients
for (int i = 0; i <= 6; i++) {
cj[i][j] = 0.;
sj[i][j] = 0.;
}
if (j < jMax) {
// initialise the C<sup>j</sup><sub>,λ</sub> and S<sup>j</sup><sub>,λ</sub> coefficients
cjlambda[j] = 0.;
sjlambda[j] = 0.;
}
for (int s = 0; s <= sMax; s++) {
// Compute the coefficients A<sub>j, s</sub>, B<sub>j, s</sub>, D<sub>j, s</sub> and E<sub>j, s</sub>
ABDECoefficients.computeCoefficients(j, s);
// compute starting value for n
final int minN = FastMath.max(2, FastMath.max(j - 1, s));
for (int n = minN; n <= nMax; n++) {
// check if n-s is even
if ((n - s) % 2 == 0) {
// compute the coefficient e<sup>-|j-s|</sup>*w<sub>j</sub><sup>n+1, s</sup> and its derivatives
final double[] wjnp1semjms = wnsjEtomjmsCoefficient.computeWjnsEmjmsAndDeriv(j, s, n + 1, context);
// compute the coefficient e<sup>-|j-s|</sup>*w<sub>-j</sub><sup>n+1, s</sup> and its derivatives
final double[] wmjnp1semjms = wnsjEtomjmsCoefficient.computeWjnsEmjmsAndDeriv(-j, s, n + 1, context);
// compute common factors
final double coef1 = -(wjnp1semjms[0] * ABDECoefficients.getCoefA() + wmjnp1semjms[0] * ABDECoefficients.getCoefB());
final double coef2 = wjnp1semjms[0] * ABDECoefficients.getCoefD() + wmjnp1semjms[0] * ABDECoefficients.getCoefE();
//Compute C<sup>j</sup>
cj[0][j] += gns.getGns(n, s) * coef1;
//Compute dC<sup>j</sup> / da
cj[1][j] += gns.getdGnsda(n, s) * coef1;
//Compute dC<sup>j</sup> / dk
cj[2][j] += -gns.getGns(n, s) *
(
wjnp1semjms[1] * ABDECoefficients.getCoefA() +
wjnp1semjms[0] * ABDECoefficients.getdCoefAdk() +
wmjnp1semjms[1] * ABDECoefficients.getCoefB() +
wmjnp1semjms[0] * ABDECoefficients.getdCoefBdk()
);
//Compute dC<sup>j</sup> / dh
cj[3][j] += -gns.getGns(n, s) *
(
wjnp1semjms[2] * ABDECoefficients.getCoefA() +
wjnp1semjms[0] * ABDECoefficients.getdCoefAdh() +
wmjnp1semjms[2] * ABDECoefficients.getCoefB() +
wmjnp1semjms[0] * ABDECoefficients.getdCoefBdh()
);
//Compute dC<sup>j</sup> / dα
cj[4][j] += -gns.getGns(n, s) *
(
wjnp1semjms[0] * ABDECoefficients.getdCoefAdalpha() +
wmjnp1semjms[0] * ABDECoefficients.getdCoefBdalpha()
);
//Compute dC<sup>j</sup> / dβ
cj[5][j] += -gns.getGns(n, s) *
(
wjnp1semjms[0] * ABDECoefficients.getdCoefAdbeta() +
wmjnp1semjms[0] * ABDECoefficients.getdCoefBdbeta()
);
//Compute dC<sup>j</sup> / dγ
cj[6][j] += gns.getdGnsdgamma(n, s) * coef1;
//Compute S<sup>j</sup>
sj[0][j] += gns.getGns(n, s) * coef2;
//Compute dS<sup>j</sup> / da
sj[1][j] += gns.getdGnsda(n, s) * coef2;
//Compute dS<sup>j</sup> / dk
sj[2][j] += gns.getGns(n, s) *
(
wjnp1semjms[1] * ABDECoefficients.getCoefD() +
wjnp1semjms[0] * ABDECoefficients.getdCoefDdk() +
wmjnp1semjms[1] * ABDECoefficients.getCoefE() +
wmjnp1semjms[0] * ABDECoefficients.getdCoefEdk()
);
//Compute dS<sup>j</sup> / dh
sj[3][j] += gns.getGns(n, s) *
(
wjnp1semjms[2] * ABDECoefficients.getCoefD() +
wjnp1semjms[0] * ABDECoefficients.getdCoefDdh() +
wmjnp1semjms[2] * ABDECoefficients.getCoefE() +
wmjnp1semjms[0] * ABDECoefficients.getdCoefEdh()
);
//Compute dS<sup>j</sup> / dα
sj[4][j] += gns.getGns(n, s) *
(
wjnp1semjms[0] * ABDECoefficients.getdCoefDdalpha() +
wmjnp1semjms[0] * ABDECoefficients.getdCoefEdalpha()
);
//Compute dS<sup>j</sup> / dβ
sj[5][j] += gns.getGns(n, s) *
(
wjnp1semjms[0] * ABDECoefficients.getdCoefDdbeta() +
wmjnp1semjms[0] * ABDECoefficients.getdCoefEdbeta()
);
//Compute dS<sup>j</sup> / dγ
sj[6][j] += gns.getdGnsdgamma(n, s) * coef2;
//Check if n is greater or equal to j and j is at most jMax-1
if (n >= j && j < jMax) {
// compute the coefficient e<sup>-|j-s|</sup>*w<sub>j</sub><sup>n, s</sup> and its derivatives
final double[] wjnsemjms = wnsjEtomjmsCoefficient.computeWjnsEmjmsAndDeriv(j, s, n, context);
// compute the coefficient e<sup>-|j-s|</sup>*w<sub>-j</sub><sup>n, s</sup> and its derivatives
final double[] wmjnsemjms = wnsjEtomjmsCoefficient.computeWjnsEmjmsAndDeriv(-j, s, n, context);
//Compute C<sup>j</sup><sub>,λ</sub>
cjlambda[j] += gns.getGns(n, s) * (wjnsemjms[0] * ABDECoefficients.getCoefD() + wmjnsemjms[0] * ABDECoefficients.getCoefE());
//Compute S<sup>j</sup><sub>,λ</sub>
sjlambda[j] += gns.getGns(n, s) * (wjnsemjms[0] * ABDECoefficients.getCoefA() + wmjnsemjms[0] * ABDECoefficients.getCoefB());
}
}
}
}
// Divide by j
for (int i = 0; i <= 6; i++) {
cj[i][j] /= j;
sj[i][j] /= j;
}
}
//The C⁰ coefficients are not computed here.
//They are evaluated at the final point.
//C⁰<sub>,λ</sub>
cjlambda[0] = auxiliaryElements.getK() * cjlambda[1] / 2. + auxiliaryElements.getH() * sjlambda[1] / 2.;
}
/** Get the Fourier coefficient C<sup>j</sup>.
* @param j j index
* @return C<sup>j</sup>
*/
public double getCj(final int j) {
return cj[0][j];
}
/** Get the derivative dC<sup>j</sup>/da.
* @param j j index
* @return dC<sup>j</sup>/da
*/
public double getdCjda(final int j) {
return cj[1][j];
}
/** Get the derivative dC<sup>j</sup>/dk.
* @param j j index
* @return dC<sup>j</sup>/dk
*/
public double getdCjdk(final int j) {
return cj[2][j];
}
/** Get the derivative dC<sup>j</sup>/dh.
* @param j j index
* @return dC<sup>j</sup>/dh
*/
public double getdCjdh(final int j) {
return cj[3][j];
}
/** Get the derivative dC<sup>j</sup>/dα.
* @param j j index
* @return dC<sup>j</sup>/dα
*/
public double getdCjdalpha(final int j) {
return cj[4][j];
}
/** Get the derivative dC<sup>j</sup>/dβ.
* @param j j index
* @return dC<sup>j</sup>/dβ
*/
public double getdCjdbeta(final int j) {
return cj[5][j];
}
/** Get the derivative dC<sup>j</sup>/dγ.
* @param j j index
* @return dC<sup>j</sup>/dγ
*/
public double getdCjdgamma(final int j) {
return cj[6][j];
}
/** Get the Fourier coefficient S<sup>j</sup>.
* @param j j index
* @return S<sup>j</sup>
*/
public double getSj(final int j) {
return sj[0][j];
}
/** Get the derivative dS<sup>j</sup>/da.
* @param j j index
* @return dS<sup>j</sup>/da
*/
public double getdSjda(final int j) {
return sj[1][j];
}
/** Get the derivative dS<sup>j</sup>/dk.
* @param j j index
* @return dS<sup>j</sup>/dk
*/
public double getdSjdk(final int j) {
return sj[2][j];
}
/** Get the derivative dS<sup>j</sup>/dh.
* @param j j index
* @return dS<sup>j</sup>/dh
*/
public double getdSjdh(final int j) {
return sj[3][j];
}
/** Get the derivative dS<sup>j</sup>/dα.
* @param j j index
* @return dS<sup>j</sup>/dα
*/
public double getdSjdalpha(final int j) {
return sj[4][j];
}
/** Get the derivative dS<sup>j</sup>/dβ.
* @param j j index
* @return dS<sup>j</sup>/dβ
*/
public double getdSjdbeta(final int j) {
return sj[5][j];
}
/** Get the derivative dS<sup>j</sup>/dγ.
* @param j j index
* @return dS<sup>j</sup>/dγ
*/
public double getdSjdgamma(final int j) {
return sj[6][j];
}
/** Get the coefficient C⁰<sub>,λ</sub>.
* @return C⁰<sub>,λ</sub>
*/
public double getC0Lambda() {
return cjlambda[0];
}
/** Get the coefficient C<sup>j</sup><sub>,λ</sub>.
* @param j j index
* @return C<sup>j</sup><sub>,λ</sub>
*/
public double getCjLambda(final int j) {
if (j < 1 || j >= jMax) {
return 0.;
}
return cjlambda[j];
}
/** Get the coefficient S<sup>j</sup><sub>,λ</sub>.
* @param j j index
* @return S<sup>j</sup><sub>,λ</sub>
*/
public double getSjLambda(final int j) {
if (j < 1 || j >= jMax) {
return 0.;
}
return sjlambda[j];
}
}
/** Computes the C<sup>j</sup> and S<sup>j</sup> coefficients Danielson 4.2-(15,16)
* and their derivatives.
* <p>
* CS Mathematical Report $3.5.3.2
* </p>
*/
private class FieldFourierCjSjCoefficients <T extends CalculusFieldElement<T>> {
/** The coefficients G<sub>n, s</sub> and their derivatives. */
private final FieldGnsCoefficients<T> gns;
/** the coefficients e<sup>-|j-s|</sup>*w<sub>j</sub><sup>n, s</sup> and their derivatives by h and k. */
private final FieldWnsjEtomjmsCoefficient<T> wnsjEtomjmsCoefficient;
/** The terms containing the coefficients C<sub>j</sub> and S<sub>j</sub> of (α, β) or (k, h). */
private final FieldCjSjAlphaBetaKH<T> ABDECoefficients;
/** The Fourier coefficients C<sup>j</sup> and their derivatives.
* <p>
* Each column of the matrix contains the following values: <br/>
* - C<sup>j</sup> <br/>
* - dC<sup>j</sup> / da <br/>
* - dC<sup>j</sup> / dk <br/>
* - dC<sup>j</sup> / dh <br/>
* - dC<sup>j</sup> / dα <br/>
* - dC<sup>j</sup> / dβ <br/>
* - dC<sup>j</sup> / dγ <br/>
* </p>
*/
private final T[][] cj;
/** The S<sup>j</sup> coefficients and their derivatives.
* <p>
* Each column of the matrix contains the following values: <br/>
* - S<sup>j</sup> <br/>
* - dS<sup>j</sup> / da <br/>
* - dS<sup>j</sup> / dk <br/>
* - dS<sup>j</sup> / dh <br/>
* - dS<sup>j</sup> / dα <br/>
* - dS<sup>j</sup> / dβ <br/>
* - dS<sup>j</sup> / dγ <br/>
* </p>
*/
private final T[][] sj;
/** The Coefficients C<sup>j</sup><sub>,λ</sub>.
* <p>
* See Danielson 4.2-21
* </p>
*/
private final T[] cjlambda;
/** The Coefficients S<sup>j</sup><sub>,λ</sub>.
* <p>
* See Danielson 4.2-21
* </p>
*/
private final T[] sjlambda;
/** Zero. */
private final T zero;
/** Maximum value for n. */
private final int nMax;
/** Maximum value for s. */
private final int sMax;
/** Maximum value for j. */
private final int jMax;
/**
* Private constructor.
*
* @param nMax maximum value for n index
* @param sMax maximum value for s index
* @param jMax maximum value for j index
* @param context container for dynamic force model attributes
* @param aoR3Pow a / R3 up to power maxAR3Pow
* @param qns Qns coefficients
* @param field field used by default
*/
FieldFourierCjSjCoefficients(final int nMax, final int sMax, final int jMax,
final FieldDSSTThirdBodyDynamicContext<T> context,
final T[] aoR3Pow, final T[][] qns,
final Field<T> field) {
//Zero
this.zero = field.getZero();
//Save parameters
this.nMax = nMax;
this.sMax = sMax;
this.jMax = jMax;
//Create objects
wnsjEtomjmsCoefficient = new FieldWnsjEtomjmsCoefficient<>(context, field);
ABDECoefficients = new FieldCjSjAlphaBetaKH<>(context, field);
gns = new FieldGnsCoefficients<>(nMax, sMax, context, aoR3Pow, qns, field);
//create arays
this.cj = MathArrays.buildArray(field, 7, jMax + 1);
this.sj = MathArrays.buildArray(field, 7, jMax + 1);
this.cjlambda = MathArrays.buildArray(field, jMax);
this.sjlambda = MathArrays.buildArray(field, jMax);
computeCoefficients(context, field);
}
/**
* Compute all coefficients.
* @param context container for attributes
* @param field field used by default
*/
private void computeCoefficients(final FieldDSSTThirdBodyDynamicContext<T> context,
final Field<T> field) {
final FieldAuxiliaryElements<T> auxiliaryElements = context.getFieldAuxiliaryElements();
for (int j = 1; j <= jMax; j++) {
// initialise the coefficients
for (int i = 0; i <= 6; i++) {
cj[i][j] = zero;
sj[i][j] = zero;
}
if (j < jMax) {
// initialise the C<sup>j</sup><sub>,λ</sub> and S<sup>j</sup><sub>,λ</sub> coefficients
cjlambda[j] = zero;
sjlambda[j] = zero;
}
for (int s = 0; s <= sMax; s++) {
// Compute the coefficients A<sub>j, s</sub>, B<sub>j, s</sub>, D<sub>j, s</sub> and E<sub>j, s</sub>
ABDECoefficients.computeCoefficients(j, s);
// compute starting value for n
final int minN = FastMath.max(2, FastMath.max(j - 1, s));
for (int n = minN; n <= nMax; n++) {
// check if n-s is even
if ((n - s) % 2 == 0) {
// compute the coefficient e<sup>-|j-s|</sup>*w<sub>j</sub><sup>n+1, s</sup> and its derivatives
final T[] wjnp1semjms = wnsjEtomjmsCoefficient.computeWjnsEmjmsAndDeriv(j, s, n + 1, context, field);
// compute the coefficient e<sup>-|j-s|</sup>*w<sub>-j</sub><sup>n+1, s</sup> and its derivatives
final T[] wmjnp1semjms = wnsjEtomjmsCoefficient.computeWjnsEmjmsAndDeriv(-j, s, n + 1, context, field);
// compute common factors
final T coef1 = (wjnp1semjms[0].multiply(ABDECoefficients.getCoefA()).add(wmjnp1semjms[0].multiply(ABDECoefficients.getCoefB()))).negate();
final T coef2 = wjnp1semjms[0].multiply(ABDECoefficients.getCoefD()).add(wmjnp1semjms[0].multiply(ABDECoefficients.getCoefE()));
//Compute C<sup>j</sup>
cj[0][j] = cj[0][j].add(gns.getGns(n, s).multiply(coef1));
//Compute dC<sup>j</sup> / da
cj[1][j] = cj[1][j].add(gns.getdGnsda(n, s).multiply(coef1));
//Compute dC<sup>j</sup> / dk
cj[2][j] = cj[2][j].add(gns.getGns(n, s).negate().
multiply(
wjnp1semjms[1].multiply(ABDECoefficients.getCoefA()).
add(wjnp1semjms[0].multiply(ABDECoefficients.getdCoefAdk())).
add(wmjnp1semjms[1].multiply(ABDECoefficients.getCoefB())).
add(wmjnp1semjms[0].multiply(ABDECoefficients.getdCoefBdk()))
));
//Compute dC<sup>j</sup> / dh
cj[3][j] = cj[3][j].add(gns.getGns(n, s).negate().
multiply(
wjnp1semjms[2].multiply(ABDECoefficients.getCoefA()).
add(wjnp1semjms[0].multiply(ABDECoefficients.getdCoefAdh())).
add(wmjnp1semjms[2].multiply(ABDECoefficients.getCoefB())).
add(wmjnp1semjms[0].multiply(ABDECoefficients.getdCoefBdh()))
));
//Compute dC<sup>j</sup> / dα
cj[4][j] = cj[4][j].add(gns.getGns(n, s).negate().
multiply(
wjnp1semjms[0].multiply(ABDECoefficients.getdCoefAdalpha()).
add(wmjnp1semjms[0].multiply(ABDECoefficients.getdCoefBdalpha()))
));
//Compute dC<sup>j</sup> / dβ
cj[5][j] = cj[5][j].add(gns.getGns(n, s).negate().
multiply(
wjnp1semjms[0].multiply(ABDECoefficients.getdCoefAdbeta()).
add(wmjnp1semjms[0].multiply(ABDECoefficients.getdCoefBdbeta()))
));
//Compute dC<sup>j</sup> / dγ
cj[6][j] = cj[6][j].add(gns.getdGnsdgamma(n, s).multiply(coef1));
//Compute S<sup>j</sup>
sj[0][j] = sj[0][j].add(gns.getGns(n, s).multiply(coef2));
//Compute dS<sup>j</sup> / da
sj[1][j] = sj[1][j].add(gns.getdGnsda(n, s).multiply(coef2));
//Compute dS<sup>j</sup> / dk
sj[2][j] = sj[2][j].add(gns.getGns(n, s).
multiply(
wjnp1semjms[1].multiply(ABDECoefficients.getCoefD()).
add(wjnp1semjms[0].multiply(ABDECoefficients.getdCoefDdk())).
add(wmjnp1semjms[1].multiply(ABDECoefficients.getCoefE())).
add(wmjnp1semjms[0].multiply(ABDECoefficients.getdCoefEdk()))
));
//Compute dS<sup>j</sup> / dh
sj[3][j] = sj[3][j].add(gns.getGns(n, s).
multiply(
wjnp1semjms[2].multiply(ABDECoefficients.getCoefD()).
add(wjnp1semjms[0].multiply(ABDECoefficients.getdCoefDdh())).
add(wmjnp1semjms[2].multiply(ABDECoefficients.getCoefE())).
add(wmjnp1semjms[0].multiply(ABDECoefficients.getdCoefEdh()))
));
//Compute dS<sup>j</sup> / dα
sj[4][j] = sj[4][j].add(gns.getGns(n, s).
multiply(
wjnp1semjms[0].multiply(ABDECoefficients.getdCoefDdalpha()).
add(wmjnp1semjms[0].multiply(ABDECoefficients.getdCoefEdalpha()))
));
//Compute dS<sup>j</sup> / dβ
sj[5][j] = sj[5][j].add(gns.getGns(n, s).
multiply(
wjnp1semjms[0].multiply(ABDECoefficients.getdCoefDdbeta()).
add(wmjnp1semjms[0].multiply(ABDECoefficients.getdCoefEdbeta()))
));
//Compute dS<sup>j</sup> / dγ
sj[6][j] = sj[6][j].add(gns.getdGnsdgamma(n, s).multiply(coef2));
//Check if n is greater or equal to j and j is at most jMax-1
if (n >= j && j < jMax) {
// compute the coefficient e<sup>-|j-s|</sup>*w<sub>j</sub><sup>n, s</sup> and its derivatives
final T[] wjnsemjms = wnsjEtomjmsCoefficient.computeWjnsEmjmsAndDeriv(j, s, n, context, field);
// compute the coefficient e<sup>-|j-s|</sup>*w<sub>-j</sub><sup>n, s</sup> and its derivatives
final T[] wmjnsemjms = wnsjEtomjmsCoefficient.computeWjnsEmjmsAndDeriv(-j, s, n, context, field);
//Compute C<sup>j</sup><sub>,λ</sub>
cjlambda[j] = cjlambda[j].add(gns.getGns(n, s).multiply(wjnsemjms[0].multiply(ABDECoefficients.getCoefD()).add(wmjnsemjms[0].multiply(ABDECoefficients.getCoefE()))));
//Compute S<sup>j</sup><sub>,λ</sub>
sjlambda[j] = sjlambda[j].add(gns.getGns(n, s).multiply(wjnsemjms[0].multiply(ABDECoefficients.getCoefA()).add(wmjnsemjms[0].multiply(ABDECoefficients.getCoefB()))));
}
}
}
}
// Divide by j
for (int i = 0; i <= 6; i++) {
cj[i][j] = cj[i][j].divide(j);
sj[i][j] = sj[i][j].divide(j);
}
}
//The C⁰ coefficients are not computed here.
//They are evaluated at the final point.
//C⁰<sub>,λ</sub>
cjlambda[0] = auxiliaryElements.getK().multiply(cjlambda[1]).divide(2.).add(auxiliaryElements.getH().multiply(sjlambda[1]).divide(2.));
}
/** Get the Fourier coefficient C<sup>j</sup>.
* @param j j index
* @return C<sup>j</sup>
*/
public T getCj(final int j) {
return cj[0][j];
}
/** Get the derivative dC<sup>j</sup>/da.
* @param j j index
* @return dC<sup>j</sup>/da
*/
public T getdCjda(final int j) {
return cj[1][j];
}
/** Get the derivative dC<sup>j</sup>/dk.
* @param j j index
* @return dC<sup>j</sup>/dk
*/
public T getdCjdk(final int j) {
return cj[2][j];
}
/** Get the derivative dC<sup>j</sup>/dh.
* @param j j index
* @return dC<sup>j</sup>/dh
*/
public T getdCjdh(final int j) {
return cj[3][j];
}
/** Get the derivative dC<sup>j</sup>/dα.
* @param j j index
* @return dC<sup>j</sup>/dα
*/
public T getdCjdalpha(final int j) {
return cj[4][j];
}
/** Get the derivative dC<sup>j</sup>/dβ.
* @param j j index
* @return dC<sup>j</sup>/dβ
*/
public T getdCjdbeta(final int j) {
return cj[5][j];
}
/** Get the derivative dC<sup>j</sup>/dγ.
* @param j j index
* @return dC<sup>j</sup>/dγ
*/
public T getdCjdgamma(final int j) {
return cj[6][j];
}
/** Get the Fourier coefficient S<sup>j</sup>.
* @param j j index
* @return S<sup>j</sup>
*/
public T getSj(final int j) {
return sj[0][j];
}
/** Get the derivative dS<sup>j</sup>/da.
* @param j j index
* @return dS<sup>j</sup>/da
*/
public T getdSjda(final int j) {
return sj[1][j];
}
/** Get the derivative dS<sup>j</sup>/dk.
* @param j j index
* @return dS<sup>j</sup>/dk
*/
public T getdSjdk(final int j) {
return sj[2][j];
}
/** Get the derivative dS<sup>j</sup>/dh.
* @param j j index
* @return dS<sup>j</sup>/dh
*/
public T getdSjdh(final int j) {
return sj[3][j];
}
/** Get the derivative dS<sup>j</sup>/dα.
* @param j j index
* @return dS<sup>j</sup>/dα
*/
public T getdSjdalpha(final int j) {
return sj[4][j];
}
/** Get the derivative dS<sup>j</sup>/dβ.
* @param j j index
* @return dS<sup>j</sup>/dβ
*/
public T getdSjdbeta(final int j) {
return sj[5][j];
}
/** Get the derivative dS<sup>j</sup>/dγ.
* @param j j index
* @return dS<sup>j</sup>/dγ
*/
public T getdSjdgamma(final int j) {
return sj[6][j];
}
/** Get the coefficient C⁰<sub>,λ</sub>.
* @return C⁰<sub>,λ</sub>
*/
public T getC0Lambda() {
return cjlambda[0];
}
/** Get the coefficient C<sup>j</sup><sub>,λ</sub>.
* @param j j index
* @return C<sup>j</sup><sub>,λ</sub>
*/
public T getCjLambda(final int j) {
if (j < 1 || j >= jMax) {
return zero;
}
return cjlambda[j];
}
/** Get the coefficient S<sup>j</sup><sub>,λ</sub>.
* @param j j index
* @return S<sup>j</sup><sub>,λ</sub>
*/
public T getSjLambda(final int j) {
if (j < 1 || j >= jMax) {
return zero;
}
return sjlambda[j];
}
}
/** This class covers the coefficients e<sup>-|j-s|</sup>*w<sub>j</sub><sup>n, s</sup> and their derivatives by h and k.
*
* <p>
* Starting from Danielson 4.2-9,10,11 and taking into account that fact that: <br />
* c = e / (1 + (1 - e²)<sup>1/2</sup>) = e / (1 + B) = e * b <br/>
* the expression e<sup>-|j-s|</sup>*w<sub>j</sub><sup>n, s</sup>
* can be written as: <br/ >
* - for |s| > |j| <br />
* e<sup>-|j-s|</sup>*w<sub>j</sub><sup>n, s</sup> =
* (((n + s)!(n - s)!)/((n + j)!(n - j)!)) *
* (-b)<sup>|j-s|</sup> *
* ((1 - c²)<sup>n-|s|</sup>/(1 + c²)<sup>n</sup>) *
* P<sub>n-|s|</sub><sup>|j-s|, |j+s|</sup>(χ) <br />
* <br />
* - for |s| <= |j| <br />
* e<sup>-|j-s|</sup>*w<sub>j</sub><sup>n, s</sup> =
* (-b)<sup>|j-s|</sup> *
* ((1 - c²)<sup>n-|j|</sup>/(1 + c²)<sup>n</sup>) *
* P<sub>n-|j|</sub><sup>|j-s|, |j+s|</sup>(χ)
* </p>
*
* @author Lucian Barbulescu
*/
private class WnsjEtomjmsCoefficient {
/** The value c.
* <p>
* c = e / (1 + (1 - e²)<sup>1/2</sup>) = e / (1 + B) = e * b <br/>
* </p>
* */
private final double c;
/** db / dh. */
private final double dbdh;
/** db / dk. */
private final double dbdk;
/** dc / dh = e * db/dh + b * de/dh. */
private final double dcdh;
/** dc / dk = e * db/dk + b * de/dk. */
private final double dcdk;
/** The values (1 - c²)<sup>n</sup>. <br />
* The maximum possible value for the power is N + 1 */
private final double[] omc2tn;
/** The values (1 + c²)<sup>n</sup>. <br />
* The maximum possible value for the power is N + 1 */
private final double[] opc2tn;
/** The values b<sup>|j-s|</sup>. */
private final double[] btjms;
/**
* Standard constructor.
* @param context container for attributes
*/
WnsjEtomjmsCoefficient(final DSSTThirdBodyDynamicContext context) {
final AuxiliaryElements auxiliaryElements = context.getAuxiliaryElements();
//initialise fields
c = auxiliaryElements.getEcc() * context.getb();
final double c2 = c * c;
//b² * χ
final double b2Chi = context.getb() * context.getb() * context.getX();
//Compute derivatives of b
dbdh = auxiliaryElements.getH() * b2Chi;
dbdk = auxiliaryElements.getK() * b2Chi;
//Compute derivatives of c
if (auxiliaryElements.getEcc() == 0.0) {
// we are at a perfectly circular orbit singularity here
// we arbitrarily consider the perigee is along the X axis,
// i.e cos(ω + Ω) = h/ecc 1 and sin(ω + Ω) = k/ecc = 0
dcdh = auxiliaryElements.getEcc() * dbdh + context.getb();
dcdk = auxiliaryElements.getEcc() * dbdk;
} else {
dcdh = auxiliaryElements.getEcc() * dbdh + context.getb() * auxiliaryElements.getH() / auxiliaryElements.getEcc();
dcdk = auxiliaryElements.getEcc() * dbdk + context.getb() * auxiliaryElements.getK() / auxiliaryElements.getEcc();
}
//Compute the powers (1 - c²)<sup>n</sup> and (1 + c²)<sup>n</sup>
omc2tn = new double[staticContext.getMaxAR3Pow() + staticContext.getMaxFreqF() + 2];
opc2tn = new double[staticContext.getMaxAR3Pow() + staticContext.getMaxFreqF() + 2];
final double omc2 = 1. - c2;
final double opc2 = 1. + c2;
omc2tn[0] = 1.;
opc2tn[0] = 1.;
for (int i = 1; i <= staticContext.getMaxAR3Pow() + staticContext.getMaxFreqF() + 1; i++) {
omc2tn[i] = omc2tn[i - 1] * omc2;
opc2tn[i] = opc2tn[i - 1] * opc2;
}
//Compute the powers of b
btjms = new double[staticContext.getMaxAR3Pow() + staticContext.getMaxFreqF() + 1];
btjms[0] = 1.;
for (int i = 1; i <= staticContext.getMaxAR3Pow() + staticContext.getMaxFreqF(); i++) {
btjms[i] = btjms[i - 1] * context.getb();
}
}
/** Compute the value of the coefficient e<sup>-|j-s|</sup>*w<sub>j</sub><sup>n, s</sup> and its derivatives by h and k. <br />
*
* @param j j index
* @param s s index
* @param n n index
* @param context container for attributes
* @return an array containing the value of the coefficient at index 0, the derivative by k at index 1 and the derivative by h at index 2
*/
public double[] computeWjnsEmjmsAndDeriv(final int j, final int s, final int n, final DSSTThirdBodyDynamicContext context) {
final double[] wjnsemjms = new double[] {0., 0., 0.};
// |j|
final int absJ = FastMath.abs(j);
// |s|
final int absS = FastMath.abs(s);
// |j - s|
final int absJmS = FastMath.abs(j - s);
// |j + s|
final int absJpS = FastMath.abs(j + s);
//The lower index of P. Also the power of (1 - c²)
final int l;
// the factorial ratio coefficient or 1. if |s| <= |j|
final double factCoef;
if (absS > absJ) {
//factCoef = (fact[n + s] / fact[n + j]) * (fact[n - s] / fact[n - j]);
factCoef = (CombinatoricsUtils.factorialDouble(n + s) / CombinatoricsUtils.factorialDouble(n + j)) * (CombinatoricsUtils.factorialDouble(n - s) / CombinatoricsUtils.factorialDouble(n - j));
l = n - absS;
} else {
factCoef = 1.;
l = n - absJ;
}
// (-1)<sup>|j-s|</sup>
final double sign = absJmS % 2 != 0 ? -1. : 1.;
//(1 - c²)<sup>n-|s|</sup> / (1 + c²)<sup>n</sup>
final double coef1 = omc2tn[l] / opc2tn[n];
//-b<sup>|j-s|</sup>
final double coef2 = sign * btjms[absJmS];
// P<sub>l</sub><sup>|j-s|, |j+s|</sup>(χ)
// Jacobi polynomial value (0) and first-order derivative (1)
final double[] jac = JacobiPolynomials.getValueAndDerivative(l, absJmS, absJpS, context.getX());
// the derivative of coef1 by c
final double dcoef1dc = -coef1 * 2. * c * (((double) n) / opc2tn[1] + ((double) l) / omc2tn[1]);
// the derivative of coef1 by h
final double dcoef1dh = dcoef1dc * dcdh;
// the derivative of coef1 by k
final double dcoef1dk = dcoef1dc * dcdk;
// the derivative of coef2 by b
final double dcoef2db = absJmS == 0 ? 0 : sign * (double) absJmS * btjms[absJmS - 1];
// the derivative of coef2 by h
final double dcoef2dh = dcoef2db * dbdh;
// the derivative of coef2 by k
final double dcoef2dk = dcoef2db * dbdk;
// the jacobi polynomial value
// final double jacobi = jac.getValue();
final double jacobi = jac[0];
// the derivative of the Jacobi polynomial by h
//final double djacobidh = jac.getGradient()[0] * context.getHXXX();
final double djacobidh = jac[1] * context.getHXXX();
// the derivative of the Jacobi polynomial by k
//final double djacobidk = jac.getGradient()[0] * context.getKXXX();
final double djacobidk = jac[1] * context.getKXXX();
//group the above coefficients to limit the mathematical operations
final double term1 = factCoef * coef1 * coef2;
final double term2 = factCoef * coef1 * jacobi;
final double term3 = factCoef * coef2 * jacobi;
//compute e<sup>-|j-s|</sup>*w<sub>j</sub><sup>n, s</sup> and its derivatives by k and h
wjnsemjms[0] = term1 * jacobi;
wjnsemjms[1] = dcoef1dk * term3 + dcoef2dk * term2 + djacobidk * term1;
wjnsemjms[2] = dcoef1dh * term3 + dcoef2dh * term2 + djacobidh * term1;
return wjnsemjms;
}
}
/** This class covers the coefficients e<sup>-|j-s|</sup>*w<sub>j</sub><sup>n, s</sup> and their derivatives by h and k.
*
* <p>
* Starting from Danielson 4.2-9,10,11 and taking into account that fact that: <br />
* c = e / (1 + (1 - e²)<sup>1/2</sup>) = e / (1 + B) = e * b <br/>
* the expression e<sup>-|j-s|</sup>*w<sub>j</sub><sup>n, s</sup>
* can be written as: <br/ >
* - for |s| > |j| <br />
* e<sup>-|j-s|</sup>*w<sub>j</sub><sup>n, s</sup> =
* (((n + s)!(n - s)!)/((n + j)!(n - j)!)) *
* (-b)<sup>|j-s|</sup> *
* ((1 - c²)<sup>n-|s|</sup>/(1 + c²)<sup>n</sup>) *
* P<sub>n-|s|</sub><sup>|j-s|, |j+s|</sup>(χ) <br />
* <br />
* - for |s| <= |j| <br />
* e<sup>-|j-s|</sup>*w<sub>j</sub><sup>n, s</sup> =
* (-b)<sup>|j-s|</sup> *
* ((1 - c²)<sup>n-|j|</sup>/(1 + c²)<sup>n</sup>) *
* P<sub>n-|j|</sub><sup>|j-s|, |j+s|</sup>(χ)
* </p>
*
* @author Lucian Barbulescu
*/
private class FieldWnsjEtomjmsCoefficient <T extends CalculusFieldElement<T>> {
/** The value c.
* <p>
* c = e / (1 + (1 - e²)<sup>1/2</sup>) = e / (1 + B) = e * b <br/>
* </p>
* */
private final T c;
/** db / dh. */
private final T dbdh;
/** db / dk. */
private final T dbdk;
/** dc / dh = e * db/dh + b * de/dh. */
private final T dcdh;
/** dc / dk = e * db/dk + b * de/dk. */
private final T dcdk;
/** The values (1 - c²)<sup>n</sup>. <br />
* The maximum possible value for the power is N + 1 */
private final T[] omc2tn;
/** The values (1 + c²)<sup>n</sup>. <br />
* The maximum possible value for the power is N + 1 */
private final T[] opc2tn;
/** The values b<sup>|j-s|</sup>. */
private final T[] btjms;
/**
* Standard constructor.
* @param context container for attributes
* @param field field used by default
*/
FieldWnsjEtomjmsCoefficient(final FieldDSSTThirdBodyDynamicContext<T> context, final Field<T> field) {
final FieldAuxiliaryElements<T> auxiliaryElements = context.getFieldAuxiliaryElements();
//Zero
final T zero = field.getZero();
//initialise fields
c = auxiliaryElements.getEcc().multiply(context.getb());
final T c2 = c.square();
//b² * χ
final T b2Chi = context.getb().multiply(context.getb()).multiply(context.getX());
//Compute derivatives of b
dbdh = auxiliaryElements.getH().multiply(b2Chi);
dbdk = auxiliaryElements.getK().multiply(b2Chi);
//Compute derivatives of c
if (auxiliaryElements.getEcc().getReal() == 0.0) {
// we are at a perfectly circular orbit singularity here
// we arbitrarily consider the perigee is along the X axis,
// i.e cos(ω + Ω) = h/ecc 1 and sin(ω + Ω) = k/ecc = 0
dcdh = auxiliaryElements.getEcc().multiply(dbdh).add(context.getb());
dcdk = auxiliaryElements.getEcc().multiply(dbdk);
} else {
dcdh = auxiliaryElements.getEcc().multiply(dbdh).add(context.getb().multiply(auxiliaryElements.getH()).divide(auxiliaryElements.getEcc()));
dcdk = auxiliaryElements.getEcc().multiply(dbdk).add(context.getb().multiply(auxiliaryElements.getK()).divide(auxiliaryElements.getEcc()));
}
//Compute the powers (1 - c²)<sup>n</sup> and (1 + c²)<sup>n</sup>
omc2tn = MathArrays.buildArray(field, staticContext.getMaxAR3Pow() + staticContext.getMaxFreqF() + 2);
opc2tn = MathArrays.buildArray(field, staticContext.getMaxAR3Pow() + staticContext.getMaxFreqF() + 2);
final T omc2 = c2.negate().add(1.);
final T opc2 = c2.add(1.);
omc2tn[0] = zero.newInstance(1.);
opc2tn[0] = zero.newInstance(1.);
for (int i = 1; i <= staticContext.getMaxAR3Pow() + staticContext.getMaxFreqF() + 1; i++) {
omc2tn[i] = omc2tn[i - 1].multiply(omc2);
opc2tn[i] = opc2tn[i - 1].multiply(opc2);
}
//Compute the powers of b
btjms = MathArrays.buildArray(field, staticContext.getMaxAR3Pow() + staticContext.getMaxFreqF() + 1);
btjms[0] = zero.newInstance(1.);
for (int i = 1; i <= staticContext.getMaxAR3Pow() + staticContext.getMaxFreqF(); i++) {
btjms[i] = btjms[i - 1].multiply(context.getb());
}
}
/** Compute the value of the coefficient e<sup>-|j-s|</sup>*w<sub>j</sub><sup>n, s</sup> and its derivatives by h and k. <br />
*
* @param j j index
* @param s s index
* @param n n index
* @param context container for attributes
* @param field field used by default
* @return an array containing the value of the coefficient at index 0, the derivative by k at index 1 and the derivative by h at index 2
*/
public T[] computeWjnsEmjmsAndDeriv(final int j, final int s, final int n,
final FieldDSSTThirdBodyDynamicContext<T> context,
final Field<T> field) {
//Zero
final T zero = field.getZero();
final T[] wjnsemjms = MathArrays.buildArray(field, 3);
Arrays.fill(wjnsemjms, zero);
// |j|
final int absJ = FastMath.abs(j);
// |s|
final int absS = FastMath.abs(s);
// |j - s|
final int absJmS = FastMath.abs(j - s);
// |j + s|
final int absJpS = FastMath.abs(j + s);
//The lower index of P. Also the power of (1 - c²)
final int l;
// the factorial ratio coefficient or 1. if |s| <= |j|
final T factCoef;
if (absS > absJ) {
//factCoef = (fact[n + s] / fact[n + j]) * (fact[n - s] / fact[n - j]);
factCoef = zero.newInstance((CombinatoricsUtils.factorialDouble(n + s) / CombinatoricsUtils.factorialDouble(n + j)) * (CombinatoricsUtils.factorialDouble(n - s) / CombinatoricsUtils.factorialDouble(n - j)));
l = n - absS;
} else {
factCoef = zero.newInstance(1.);
l = n - absJ;
}
// (-1)<sup>|j-s|</sup>
final T sign = absJmS % 2 != 0 ? zero.newInstance(-1.) : zero.newInstance(1.);
//(1 - c²)<sup>n-|s|</sup> / (1 + c²)<sup>n</sup>
final T coef1 = omc2tn[l].divide(opc2tn[n]);
//-b<sup>|j-s|</sup>
final T coef2 = btjms[absJmS].multiply(sign);
// P<sub>l</sub><sup>|j-s|, |j+s|</sup>(χ)
final FieldGradient<T> jac =
JacobiPolynomials.getValue(l, absJmS, absJpS, FieldGradient.variable(1, 0, context.getX()));
// the derivative of coef1 by c
final T dcoef1dc = coef1.negate().multiply(2.).multiply(c).multiply(opc2tn[1].reciprocal().multiply(n).add(omc2tn[1].reciprocal().multiply(l)));
// the derivative of coef1 by h
final T dcoef1dh = dcoef1dc.multiply(dcdh);
// the derivative of coef1 by k
final T dcoef1dk = dcoef1dc.multiply(dcdk);
// the derivative of coef2 by b
final T dcoef2db = absJmS == 0 ? zero : sign.multiply(absJmS).multiply(btjms[absJmS - 1]);
// the derivative of coef2 by h
final T dcoef2dh = dcoef2db.multiply(dbdh);
// the derivative of coef2 by k
final T dcoef2dk = dcoef2db.multiply(dbdk);
// the jacobi polynomial value
final T jacobi = jac.getValue();
// the derivative of the Jacobi polynomial by h
final T djacobidh = jac.getGradient()[0].multiply(context.getHXXX());
// the derivative of the Jacobi polynomial by k
final T djacobidk = jac.getGradient()[0].multiply(context.getKXXX());
//group the above coefficients to limit the mathematical operations
final T term1 = factCoef.multiply(coef1).multiply(coef2);
final T term2 = factCoef.multiply(coef1).multiply(jacobi);
final T term3 = factCoef.multiply(coef2).multiply(jacobi);
//compute e<sup>-|j-s|</sup>*w<sub>j</sub><sup>n, s</sup> and its derivatives by k and h
wjnsemjms[0] = term1.multiply(jacobi);
wjnsemjms[1] = dcoef1dk.multiply(term3).add(dcoef2dk.multiply(term2)).add(djacobidk.multiply(term1));
wjnsemjms[2] = dcoef1dh.multiply(term3).add(dcoef2dh.multiply(term2)).add(djacobidh.multiply(term1));
return wjnsemjms;
}
}
/** The G<sub>n,s</sub> coefficients and their derivatives.
* <p>
* See Danielson, 4.2-17
*
* @author Lucian Barbulescu
*/
private class GnsCoefficients {
/** Maximum value for n index. */
private final int nMax;
/** Maximum value for s index. */
private final int sMax;
/** The coefficients G<sub>n,s</sub>. */
private final double[][] gns;
/** The derivatives of the coefficients G<sub>n,s</sub> by a. */
private final double[][] dgnsda;
/** The derivatives of the coefficients G<sub>n,s</sub> by γ. */
private final double[][] dgnsdgamma;
/** Standard constructor.
*
* @param nMax maximum value for n indes
* @param sMax maximum value for s index
* @param context container for attributes
* @param aoR3Pow a / R3 up to power maxAR3Pow
* @param qns Qns coefficients
*/
GnsCoefficients(final int nMax, final int sMax,
final DSSTThirdBodyDynamicContext context,
final double[] aoR3Pow, final double[][] qns) {
this.nMax = nMax;
this.sMax = sMax;
final int rows = nMax + 1;
final int columns = sMax + 1;
this.gns = new double[rows][columns];
this.dgnsda = new double[rows][columns];
this.dgnsdgamma = new double[rows][columns];
// Generate the coefficients
generateCoefficients(context, aoR3Pow, qns);
}
/**
* Compute the coefficient G<sub>n,s</sub> and its derivatives.
* <p>
* Only the derivatives by a and γ are computed as all others are 0
* </p>
* @param context container for attributes
* @param aoR3Pow a / R3 up to power maxAR3Pow
* @param qns Qns coefficients
*/
private void generateCoefficients(final DSSTThirdBodyDynamicContext context, final double[] aoR3Pow, final double[][] qns) {
final AuxiliaryElements auxiliaryElements = context.getAuxiliaryElements();
for (int s = 0; s <= sMax; s++) {
// The n index is always at least the maximum between 2 and s
final int minN = FastMath.max(2, s);
for (int n = minN; n <= nMax; n++) {
// compute the coefficients only if (n - s) % 2 == 0
if ( (n - s) % 2 == 0 ) {
// Kronecker symbol (2 - delta(0,s))
final double delta0s = (s == 0) ? 1. : 2.;
final double vns = Vns.get(new NSKey(n, s));
final double coef0 = delta0s * aoR3Pow[n] * vns * context.getMuoR3();
final double coef1 = coef0 * qns[n][s];
// dQns/dGamma = Q(n, s + 1) from Equation 3.1-(8)
// for n = s, Q(n, n + 1) = 0. (Cefola & Broucke, 1975)
final double dqns = (n == s) ? 0. : qns[n][s + 1];
//Compute the coefficient and its derivatives.
this.gns[n][s] = coef1;
this.dgnsda[n][s] = coef1 * n / auxiliaryElements.getSma();
this.dgnsdgamma[n][s] = coef0 * dqns;
} else {
// the coefficient and its derivatives is 0
this.gns[n][s] = 0.;
this.dgnsda[n][s] = 0.;
this.dgnsdgamma[n][s] = 0.;
}
}
}
}
/** Get the coefficient G<sub>n,s</sub>.
*
* @param n n index
* @param s s index
* @return the coefficient G<sub>n,s</sub>
*/
public double getGns(final int n, final int s) {
return this.gns[n][s];
}
/** Get the derivative dG<sub>n,s</sub> / da.
*
* @param n n index
* @param s s index
* @return the derivative dG<sub>n,s</sub> / da
*/
public double getdGnsda(final int n, final int s) {
return this.dgnsda[n][s];
}
/** Get the derivative dG<sub>n,s</sub> / dγ.
*
* @param n n index
* @param s s index
* @return the derivative dG<sub>n,s</sub> / dγ
*/
public double getdGnsdgamma(final int n, final int s) {
return this.dgnsdgamma[n][s];
}
}
/** The G<sub>n,s</sub> coefficients and their derivatives.
* <p>
* See Danielson, 4.2-17
*
* @author Lucian Barbulescu
*/
private class FieldGnsCoefficients <T extends CalculusFieldElement<T>> {
/** Maximum value for n index. */
private final int nMax;
/** Maximum value for s index. */
private final int sMax;
/** The coefficients G<sub>n,s</sub>. */
private final T[][] gns;
/** The derivatives of the coefficients G<sub>n,s</sub> by a. */
private final T[][] dgnsda;
/** The derivatives of the coefficients G<sub>n,s</sub> by γ. */
private final T[][] dgnsdgamma;
/** Standard constructor.
*
* @param nMax maximum value for n indes
* @param sMax maximum value for s index
* @param context container for attributes
* @param aoR3Pow a / R3 up to power maxAR3Pow
* @param qns Qns coefficients
* @param field field used by default
*/
FieldGnsCoefficients(final int nMax, final int sMax,
final FieldDSSTThirdBodyDynamicContext<T> context,
final T[] aoR3Pow, final T[][] qns,
final Field<T> field) {
this.nMax = nMax;
this.sMax = sMax;
final int rows = nMax + 1;
final int columns = sMax + 1;
this.gns = MathArrays.buildArray(field, rows, columns);
this.dgnsda = MathArrays.buildArray(field, rows, columns);
this.dgnsdgamma = MathArrays.buildArray(field, rows, columns);
// Generate the coefficients
generateCoefficients(context, aoR3Pow, qns, field);
}
/**
* Compute the coefficient G<sub>n,s</sub> and its derivatives.
* <p>
* Only the derivatives by a and γ are computed as all others are 0
* </p>
* @param context container for attributes
* @param aoR3Pow a / R3 up to power maxAR3Pow
* @param qns Qns coefficients
* @param field field used by default
*/
private void generateCoefficients(final FieldDSSTThirdBodyDynamicContext<T> context,
final T[] aoR3Pow, final T[][] qns,
final Field<T> field) {
//Zero
final T zero = field.getZero();
final FieldAuxiliaryElements<T> auxiliaryElements = context.getFieldAuxiliaryElements();
for (int s = 0; s <= sMax; s++) {
// The n index is always at least the maximum between 2 and s
final int minN = FastMath.max(2, s);
for (int n = minN; n <= nMax; n++) {
// compute the coefficients only if (n - s) % 2 == 0
if ( (n - s) % 2 == 0 ) {
// Kronecker symbol (2 - delta(0,s))
final T delta0s = (s == 0) ? zero.newInstance(1.) : zero.newInstance(2.);
final double vns = Vns.get(new NSKey(n, s));
final T coef0 = aoR3Pow[n].multiply(vns).multiply(context.getMuoR3()).multiply(delta0s);
final T coef1 = coef0.multiply(qns[n][s]);
// dQns/dGamma = Q(n, s + 1) from Equation 3.1-(8)
// for n = s, Q(n, n + 1) = 0. (Cefola & Broucke, 1975)
final T dqns = (n == s) ? zero : qns[n][s + 1];
//Compute the coefficient and its derivatives.
this.gns[n][s] = coef1;
this.dgnsda[n][s] = coef1.multiply(n).divide(auxiliaryElements.getSma());
this.dgnsdgamma[n][s] = coef0.multiply(dqns);
} else {
// the coefficient and its derivatives is 0
this.gns[n][s] = zero;
this.dgnsda[n][s] = zero;
this.dgnsdgamma[n][s] = zero;
}
}
}
}
/** Get the coefficient G<sub>n,s</sub>.
*
* @param n n index
* @param s s index
* @return the coefficient G<sub>n,s</sub>
*/
public T getGns(final int n, final int s) {
return this.gns[n][s];
}
/** Get the derivative dG<sub>n,s</sub> / da.
*
* @param n n index
* @param s s index
* @return the derivative dG<sub>n,s</sub> / da
*/
public T getdGnsda(final int n, final int s) {
return this.dgnsda[n][s];
}
/** Get the derivative dG<sub>n,s</sub> / dγ.
*
* @param n n index
* @param s s index
* @return the derivative dG<sub>n,s</sub> / dγ
*/
public T getdGnsdgamma(final int n, final int s) {
return this.dgnsdgamma[n][s];
}
}
/** This class computes the terms containing the coefficients C<sub>j</sub> and S<sub>j</sub> of (α, β) or (k, h).
*
* <p>
* The following terms and their derivatives by k, h, alpha and beta are considered: <br/ >
* - sign(j-s) * C<sub>s</sub>(α, β) * S<sub>|j-s|</sub>(k, h) + S<sub>s</sub>(α, β) * C<sub>|j-s|</sub>(k, h) <br />
* - C<sub>s</sub>(α, β) * S<sub>j+s</sub>(k, h) - S<sub>s</sub>(α, β) * C<sub>j+s</sub>(k, h) <br />
* - C<sub>s</sub>(α, β) * C<sub>|j-s|</sub>(k, h) - sign(j-s) * S<sub>s</sub>(α, β) * S<sub>|j-s|</sub>(k, h) <br />
* - C<sub>s</sub>(α, β) * C<sub>j+s</sub>(k, h) + S<sub>s</sub>(α, β) * S<sub>j+s</sub>(k, h) <br />
* For the ease of usage the above terms are renamed A<sub>js</sub>, B<sub>js</sub>, D<sub>js</sub> and E<sub>js</sub> respectively <br />
* See the CS Mathematical report $3.5.3.2 for more details
* </p>
* @author Lucian Barbulescu
*/
private static class CjSjAlphaBetaKH {
/** The C<sub>j</sub>(k, h) and the S<sub>j</sub>(k, h) series. */
private final CjSjCoefficient cjsjkh;
/** The C<sub>j</sub>(α, β) and the S<sub>j</sub>(α, β) series. */
private final CjSjCoefficient cjsjalbe;
/** The coeficient sign(j-s) * C<sub>s</sub>(α, β) * S<sub>|j-s|</sub>(k, h) + S<sub>s</sub>(α, β) * C<sub>|j-s|</sub>(k, h)
* and its derivative by k, h, α and β. */
private final double[] coefAandDeriv;
/** The coeficient C<sub>s</sub>(α, β) * S<sub>j+s</sub>(k, h) - S<sub>s</sub>(α, β) * C<sub>j+s</sub>(k, h)
* and its derivative by k, h, α and β. */
private final double[] coefBandDeriv;
/** The coeficient C<sub>s</sub>(α, β) * C<sub>|j-s|</sub>(k, h) - sign(j-s) * S<sub>s</sub>(α, β) * S<sub>|j-s|</sub>(k, h)
* and its derivative by k, h, α and β. */
private final double[] coefDandDeriv;
/** The coeficient C<sub>s</sub>(α, β) * C<sub>j+s</sub>(k, h) + S<sub>s</sub>(α, β) * S<sub>j+s</sub>(k, h)
* and its derivative by k, h, α and β. */
private final double[] coefEandDeriv;
/**
* Standard constructor.
* @param context container for attributes
*/
CjSjAlphaBetaKH(final DSSTThirdBodyDynamicContext context) {
final AuxiliaryElements auxiliaryElements = context.getAuxiliaryElements();
cjsjkh = new CjSjCoefficient(auxiliaryElements.getK(), auxiliaryElements.getH());
cjsjalbe = new CjSjCoefficient(context.getAlpha(), context.getBeta());
coefAandDeriv = new double[5];
coefBandDeriv = new double[5];
coefDandDeriv = new double[5];
coefEandDeriv = new double[5];
}
/** Compute the coefficients and their derivatives for a given (j,s) pair.
* @param j j index
* @param s s index
*/
public void computeCoefficients(final int j, final int s) {
// sign of j-s
final int sign = j < s ? -1 : 1;
//|j-s|
final int absJmS = FastMath.abs(j - s);
//j+s
final int jps = j + s;
//Compute the coefficient A and its derivatives
coefAandDeriv[0] = sign * cjsjalbe.getCj(s) * cjsjkh.getSj(absJmS) + cjsjalbe.getSj(s) * cjsjkh.getCj(absJmS);
coefAandDeriv[1] = sign * cjsjalbe.getCj(s) * cjsjkh.getDsjDk(absJmS) + cjsjalbe.getSj(s) * cjsjkh.getDcjDk(absJmS);
coefAandDeriv[2] = sign * cjsjalbe.getCj(s) * cjsjkh.getDsjDh(absJmS) + cjsjalbe.getSj(s) * cjsjkh.getDcjDh(absJmS);
coefAandDeriv[3] = sign * cjsjalbe.getDcjDk(s) * cjsjkh.getSj(absJmS) + cjsjalbe.getDsjDk(s) * cjsjkh.getCj(absJmS);
coefAandDeriv[4] = sign * cjsjalbe.getDcjDh(s) * cjsjkh.getSj(absJmS) + cjsjalbe.getDsjDh(s) * cjsjkh.getCj(absJmS);
//Compute the coefficient B and its derivatives
coefBandDeriv[0] = cjsjalbe.getCj(s) * cjsjkh.getSj(jps) - cjsjalbe.getSj(s) * cjsjkh.getCj(jps);
coefBandDeriv[1] = cjsjalbe.getCj(s) * cjsjkh.getDsjDk(jps) - cjsjalbe.getSj(s) * cjsjkh.getDcjDk(jps);
coefBandDeriv[2] = cjsjalbe.getCj(s) * cjsjkh.getDsjDh(jps) - cjsjalbe.getSj(s) * cjsjkh.getDcjDh(jps);
coefBandDeriv[3] = cjsjalbe.getDcjDk(s) * cjsjkh.getSj(jps) - cjsjalbe.getDsjDk(s) * cjsjkh.getCj(jps);
coefBandDeriv[4] = cjsjalbe.getDcjDh(s) * cjsjkh.getSj(jps) - cjsjalbe.getDsjDh(s) * cjsjkh.getCj(jps);
//Compute the coefficient D and its derivatives
coefDandDeriv[0] = cjsjalbe.getCj(s) * cjsjkh.getCj(absJmS) - sign * cjsjalbe.getSj(s) * cjsjkh.getSj(absJmS);
coefDandDeriv[1] = cjsjalbe.getCj(s) * cjsjkh.getDcjDk(absJmS) - sign * cjsjalbe.getSj(s) * cjsjkh.getDsjDk(absJmS);
coefDandDeriv[2] = cjsjalbe.getCj(s) * cjsjkh.getDcjDh(absJmS) - sign * cjsjalbe.getSj(s) * cjsjkh.getDsjDh(absJmS);
coefDandDeriv[3] = cjsjalbe.getDcjDk(s) * cjsjkh.getCj(absJmS) - sign * cjsjalbe.getDsjDk(s) * cjsjkh.getSj(absJmS);
coefDandDeriv[4] = cjsjalbe.getDcjDh(s) * cjsjkh.getCj(absJmS) - sign * cjsjalbe.getDsjDh(s) * cjsjkh.getSj(absJmS);
//Compute the coefficient E and its derivatives
coefEandDeriv[0] = cjsjalbe.getCj(s) * cjsjkh.getCj(jps) + cjsjalbe.getSj(s) * cjsjkh.getSj(jps);
coefEandDeriv[1] = cjsjalbe.getCj(s) * cjsjkh.getDcjDk(jps) + cjsjalbe.getSj(s) * cjsjkh.getDsjDk(jps);
coefEandDeriv[2] = cjsjalbe.getCj(s) * cjsjkh.getDcjDh(jps) + cjsjalbe.getSj(s) * cjsjkh.getDsjDh(jps);
coefEandDeriv[3] = cjsjalbe.getDcjDk(s) * cjsjkh.getCj(jps) + cjsjalbe.getDsjDk(s) * cjsjkh.getSj(jps);
coefEandDeriv[4] = cjsjalbe.getDcjDh(s) * cjsjkh.getCj(jps) + cjsjalbe.getDsjDh(s) * cjsjkh.getSj(jps);
}
/** Get the value of coefficient A<sub>j,s</sub>.
*
* @return the coefficient A<sub>j,s</sub>
*/
public double getCoefA() {
return coefAandDeriv[0];
}
/** Get the value of coefficient dA<sub>j,s</sub>/dk.
*
* @return the coefficient dA<sub>j,s</sub>/dk
*/
public double getdCoefAdk() {
return coefAandDeriv[1];
}
/** Get the value of coefficient dA<sub>j,s</sub>/dh.
*
* @return the coefficient dA<sub>j,s</sub>/dh
*/
public double getdCoefAdh() {
return coefAandDeriv[2];
}
/** Get the value of coefficient dA<sub>j,s</sub>/dα.
*
* @return the coefficient dA<sub>j,s</sub>/dα
*/
public double getdCoefAdalpha() {
return coefAandDeriv[3];
}
/** Get the value of coefficient dA<sub>j,s</sub>/dβ.
*
* @return the coefficient dA<sub>j,s</sub>/dβ
*/
public double getdCoefAdbeta() {
return coefAandDeriv[4];
}
/** Get the value of coefficient B<sub>j,s</sub>.
*
* @return the coefficient B<sub>j,s</sub>
*/
public double getCoefB() {
return coefBandDeriv[0];
}
/** Get the value of coefficient dB<sub>j,s</sub>/dk.
*
* @return the coefficient dB<sub>j,s</sub>/dk
*/
public double getdCoefBdk() {
return coefBandDeriv[1];
}
/** Get the value of coefficient dB<sub>j,s</sub>/dh.
*
* @return the coefficient dB<sub>j,s</sub>/dh
*/
public double getdCoefBdh() {
return coefBandDeriv[2];
}
/** Get the value of coefficient dB<sub>j,s</sub>/dα.
*
* @return the coefficient dB<sub>j,s</sub>/dα
*/
public double getdCoefBdalpha() {
return coefBandDeriv[3];
}
/** Get the value of coefficient dB<sub>j,s</sub>/dβ.
*
* @return the coefficient dB<sub>j,s</sub>/dβ
*/
public double getdCoefBdbeta() {
return coefBandDeriv[4];
}
/** Get the value of coefficient D<sub>j,s</sub>.
*
* @return the coefficient D<sub>j,s</sub>
*/
public double getCoefD() {
return coefDandDeriv[0];
}
/** Get the value of coefficient dD<sub>j,s</sub>/dk.
*
* @return the coefficient dD<sub>j,s</sub>/dk
*/
public double getdCoefDdk() {
return coefDandDeriv[1];
}
/** Get the value of coefficient dD<sub>j,s</sub>/dh.
*
* @return the coefficient dD<sub>j,s</sub>/dh
*/
public double getdCoefDdh() {
return coefDandDeriv[2];
}
/** Get the value of coefficient dD<sub>j,s</sub>/dα.
*
* @return the coefficient dD<sub>j,s</sub>/dα
*/
public double getdCoefDdalpha() {
return coefDandDeriv[3];
}
/** Get the value of coefficient dD<sub>j,s</sub>/dβ.
*
* @return the coefficient dD<sub>j,s</sub>/dβ
*/
public double getdCoefDdbeta() {
return coefDandDeriv[4];
}
/** Get the value of coefficient E<sub>j,s</sub>.
*
* @return the coefficient E<sub>j,s</sub>
*/
public double getCoefE() {
return coefEandDeriv[0];
}
/** Get the value of coefficient dE<sub>j,s</sub>/dk.
*
* @return the coefficient dE<sub>j,s</sub>/dk
*/
public double getdCoefEdk() {
return coefEandDeriv[1];
}
/** Get the value of coefficient dE<sub>j,s</sub>/dh.
*
* @return the coefficient dE<sub>j,s</sub>/dh
*/
public double getdCoefEdh() {
return coefEandDeriv[2];
}
/** Get the value of coefficient dE<sub>j,s</sub>/dα.
*
* @return the coefficient dE<sub>j,s</sub>/dα
*/
public double getdCoefEdalpha() {
return coefEandDeriv[3];
}
/** Get the value of coefficient dE<sub>j,s</sub>/dβ.
*
* @return the coefficient dE<sub>j,s</sub>/dβ
*/
public double getdCoefEdbeta() {
return coefEandDeriv[4];
}
}
/** This class computes the terms containing the coefficients C<sub>j</sub> and S<sub>j</sub> of (α, β) or (k, h).
*
* <p>
* The following terms and their derivatives by k, h, alpha and beta are considered: <br/ >
* - sign(j-s) * C<sub>s</sub>(α, β) * S<sub>|j-s|</sub>(k, h) + S<sub>s</sub>(α, β) * C<sub>|j-s|</sub>(k, h) <br />
* - C<sub>s</sub>(α, β) * S<sub>j+s</sub>(k, h) - S<sub>s</sub>(α, β) * C<sub>j+s</sub>(k, h) <br />
* - C<sub>s</sub>(α, β) * C<sub>|j-s|</sub>(k, h) - sign(j-s) * S<sub>s</sub>(α, β) * S<sub>|j-s|</sub>(k, h) <br />
* - C<sub>s</sub>(α, β) * C<sub>j+s</sub>(k, h) + S<sub>s</sub>(α, β) * S<sub>j+s</sub>(k, h) <br />
* For the ease of usage the above terms are renamed A<sub>js</sub>, B<sub>js</sub>, D<sub>js</sub> and E<sub>js</sub> respectively <br />
* See the CS Mathematical report $3.5.3.2 for more details
* </p>
* @author Lucian Barbulescu
*/
private static class FieldCjSjAlphaBetaKH <T extends CalculusFieldElement<T>> {
/** The C<sub>j</sub>(k, h) and the S<sub>j</sub>(k, h) series. */
private final FieldCjSjCoefficient<T> cjsjkh;
/** The C<sub>j</sub>(α, β) and the S<sub>j</sub>(α, β) series. */
private final FieldCjSjCoefficient<T> cjsjalbe;
/** The coeficient sign(j-s) * C<sub>s</sub>(α, β) * S<sub>|j-s|</sub>(k, h) + S<sub>s</sub>(α, β) * C<sub>|j-s|</sub>(k, h)
* and its derivative by k, h, α and β. */
private final T[] coefAandDeriv;
/** The coeficient C<sub>s</sub>(α, β) * S<sub>j+s</sub>(k, h) - S<sub>s</sub>(α, β) * C<sub>j+s</sub>(k, h)
* and its derivative by k, h, α and β. */
private final T[] coefBandDeriv;
/** The coeficient C<sub>s</sub>(α, β) * C<sub>|j-s|</sub>(k, h) - sign(j-s) * S<sub>s</sub>(α, β) * S<sub>|j-s|</sub>(k, h)
* and its derivative by k, h, α and β. */
private final T[] coefDandDeriv;
/** The coeficient C<sub>s</sub>(α, β) * C<sub>j+s</sub>(k, h) + S<sub>s</sub>(α, β) * S<sub>j+s</sub>(k, h)
* and its derivative by k, h, α and β. */
private final T[] coefEandDeriv;
/**
* Standard constructor.
* @param context container for attributes
* @param field field used by default
*/
FieldCjSjAlphaBetaKH(final FieldDSSTThirdBodyDynamicContext<T> context, final Field<T> field) {
final FieldAuxiliaryElements<T> auxiliaryElements = context.getFieldAuxiliaryElements();
cjsjkh = new FieldCjSjCoefficient<>(auxiliaryElements.getK(), auxiliaryElements.getH(), field);
cjsjalbe = new FieldCjSjCoefficient<>(context.getAlpha(), context.getBeta(), field);
coefAandDeriv = MathArrays.buildArray(field, 5);
coefBandDeriv = MathArrays.buildArray(field, 5);
coefDandDeriv = MathArrays.buildArray(field, 5);
coefEandDeriv = MathArrays.buildArray(field, 5);
}
/** Compute the coefficients and their derivatives for a given (j,s) pair.
* @param j j index
* @param s s index
*/
public void computeCoefficients(final int j, final int s) {
// sign of j-s
final int sign = j < s ? -1 : 1;
//|j-s|
final int absJmS = FastMath.abs(j - s);
//j+s
final int jps = j + s;
//Compute the coefficient A and its derivatives
coefAandDeriv[0] = cjsjalbe.getCj(s).multiply(cjsjkh.getSj(absJmS)).multiply(sign).add(cjsjalbe.getSj(s).multiply(cjsjkh.getCj(absJmS)));
coefAandDeriv[1] = cjsjalbe.getCj(s).multiply(cjsjkh.getDsjDk(absJmS)).multiply(sign).add(cjsjalbe.getSj(s).multiply(cjsjkh.getDcjDk(absJmS)));
coefAandDeriv[2] = cjsjalbe.getCj(s).multiply(cjsjkh.getDsjDh(absJmS)).multiply(sign).add(cjsjalbe.getSj(s).multiply(cjsjkh.getDcjDh(absJmS)));
coefAandDeriv[3] = cjsjalbe.getDcjDk(s).multiply(cjsjkh.getSj(absJmS)).multiply(sign).add(cjsjalbe.getDsjDk(s).multiply(cjsjkh.getCj(absJmS)));
coefAandDeriv[4] = cjsjalbe.getDcjDh(s).multiply(cjsjkh.getSj(absJmS)).multiply(sign).add(cjsjalbe.getDsjDh(s).multiply(cjsjkh.getCj(absJmS)));
//Compute the coefficient B and its derivatives
coefBandDeriv[0] = cjsjalbe.getCj(s).multiply(cjsjkh.getSj(jps)).subtract(cjsjalbe.getSj(s).multiply(cjsjkh.getCj(jps)));
coefBandDeriv[1] = cjsjalbe.getCj(s).multiply(cjsjkh.getDsjDk(jps)).subtract(cjsjalbe.getSj(s).multiply(cjsjkh.getDcjDk(jps)));
coefBandDeriv[2] = cjsjalbe.getCj(s).multiply(cjsjkh.getDsjDh(jps)).subtract(cjsjalbe.getSj(s).multiply(cjsjkh.getDcjDh(jps)));
coefBandDeriv[3] = cjsjalbe.getDcjDk(s).multiply(cjsjkh.getSj(jps)).subtract(cjsjalbe.getDsjDk(s).multiply(cjsjkh.getCj(jps)));
coefBandDeriv[4] = cjsjalbe.getDcjDh(s).multiply(cjsjkh.getSj(jps)).subtract(cjsjalbe.getDsjDh(s).multiply(cjsjkh.getCj(jps)));
//Compute the coefficient D and its derivatives
coefDandDeriv[0] = cjsjalbe.getCj(s).multiply(cjsjkh.getCj(absJmS)).subtract(cjsjalbe.getSj(s).multiply(cjsjkh.getSj(absJmS)).multiply(sign));
coefDandDeriv[1] = cjsjalbe.getCj(s).multiply(cjsjkh.getDcjDk(absJmS)).subtract(cjsjalbe.getSj(s).multiply(cjsjkh.getDsjDk(absJmS)).multiply(sign));
coefDandDeriv[2] = cjsjalbe.getCj(s).multiply(cjsjkh.getDcjDh(absJmS)).subtract(cjsjalbe.getSj(s).multiply(cjsjkh.getDsjDh(absJmS)).multiply(sign));
coefDandDeriv[3] = cjsjalbe.getDcjDk(s).multiply(cjsjkh.getCj(absJmS)).subtract(cjsjalbe.getDsjDk(s).multiply(cjsjkh.getSj(absJmS)).multiply(sign));
coefDandDeriv[4] = cjsjalbe.getDcjDh(s).multiply(cjsjkh.getCj(absJmS)).subtract(cjsjalbe.getDsjDh(s).multiply(cjsjkh.getSj(absJmS)).multiply(sign));
//Compute the coefficient E and its derivatives
coefEandDeriv[0] = cjsjalbe.getCj(s).multiply(cjsjkh.getCj(jps)).add(cjsjalbe.getSj(s).multiply(cjsjkh.getSj(jps)));
coefEandDeriv[1] = cjsjalbe.getCj(s).multiply(cjsjkh.getDcjDk(jps)).add(cjsjalbe.getSj(s).multiply(cjsjkh.getDsjDk(jps)));
coefEandDeriv[2] = cjsjalbe.getCj(s).multiply(cjsjkh.getDcjDh(jps)).add(cjsjalbe.getSj(s).multiply(cjsjkh.getDsjDh(jps)));
coefEandDeriv[3] = cjsjalbe.getDcjDk(s).multiply(cjsjkh.getCj(jps)).add(cjsjalbe.getDsjDk(s).multiply(cjsjkh.getSj(jps)));
coefEandDeriv[4] = cjsjalbe.getDcjDh(s).multiply(cjsjkh.getCj(jps)).add(cjsjalbe.getDsjDh(s).multiply(cjsjkh.getSj(jps)));
}
/** Get the value of coefficient A<sub>j,s</sub>.
*
* @return the coefficient A<sub>j,s</sub>
*/
public T getCoefA() {
return coefAandDeriv[0];
}
/** Get the value of coefficient dA<sub>j,s</sub>/dk.
*
* @return the coefficient dA<sub>j,s</sub>/dk
*/
public T getdCoefAdk() {
return coefAandDeriv[1];
}
/** Get the value of coefficient dA<sub>j,s</sub>/dh.
*
* @return the coefficient dA<sub>j,s</sub>/dh
*/
public T getdCoefAdh() {
return coefAandDeriv[2];
}
/** Get the value of coefficient dA<sub>j,s</sub>/dα.
*
* @return the coefficient dA<sub>j,s</sub>/dα
*/
public T getdCoefAdalpha() {
return coefAandDeriv[3];
}
/** Get the value of coefficient dA<sub>j,s</sub>/dβ.
*
* @return the coefficient dA<sub>j,s</sub>/dβ
*/
public T getdCoefAdbeta() {
return coefAandDeriv[4];
}
/** Get the value of coefficient B<sub>j,s</sub>.
*
* @return the coefficient B<sub>j,s</sub>
*/
public T getCoefB() {
return coefBandDeriv[0];
}
/** Get the value of coefficient dB<sub>j,s</sub>/dk.
*
* @return the coefficient dB<sub>j,s</sub>/dk
*/
public T getdCoefBdk() {
return coefBandDeriv[1];
}
/** Get the value of coefficient dB<sub>j,s</sub>/dh.
*
* @return the coefficient dB<sub>j,s</sub>/dh
*/
public T getdCoefBdh() {
return coefBandDeriv[2];
}
/** Get the value of coefficient dB<sub>j,s</sub>/dα.
*
* @return the coefficient dB<sub>j,s</sub>/dα
*/
public T getdCoefBdalpha() {
return coefBandDeriv[3];
}
/** Get the value of coefficient dB<sub>j,s</sub>/dβ.
*
* @return the coefficient dB<sub>j,s</sub>/dβ
*/
public T getdCoefBdbeta() {
return coefBandDeriv[4];
}
/** Get the value of coefficient D<sub>j,s</sub>.
*
* @return the coefficient D<sub>j,s</sub>
*/
public T getCoefD() {
return coefDandDeriv[0];
}
/** Get the value of coefficient dD<sub>j,s</sub>/dk.
*
* @return the coefficient dD<sub>j,s</sub>/dk
*/
public T getdCoefDdk() {
return coefDandDeriv[1];
}
/** Get the value of coefficient dD<sub>j,s</sub>/dh.
*
* @return the coefficient dD<sub>j,s</sub>/dh
*/
public T getdCoefDdh() {
return coefDandDeriv[2];
}
/** Get the value of coefficient dD<sub>j,s</sub>/dα.
*
* @return the coefficient dD<sub>j,s</sub>/dα
*/
public T getdCoefDdalpha() {
return coefDandDeriv[3];
}
/** Get the value of coefficient dD<sub>j,s</sub>/dβ.
*
* @return the coefficient dD<sub>j,s</sub>/dβ
*/
public T getdCoefDdbeta() {
return coefDandDeriv[4];
}
/** Get the value of coefficient E<sub>j,s</sub>.
*
* @return the coefficient E<sub>j,s</sub>
*/
public T getCoefE() {
return coefEandDeriv[0];
}
/** Get the value of coefficient dE<sub>j,s</sub>/dk.
*
* @return the coefficient dE<sub>j,s</sub>/dk
*/
public T getdCoefEdk() {
return coefEandDeriv[1];
}
/** Get the value of coefficient dE<sub>j,s</sub>/dh.
*
* @return the coefficient dE<sub>j,s</sub>/dh
*/
public T getdCoefEdh() {
return coefEandDeriv[2];
}
/** Get the value of coefficient dE<sub>j,s</sub>/dα.
*
* @return the coefficient dE<sub>j,s</sub>/dα
*/
public T getdCoefEdalpha() {
return coefEandDeriv[3];
}
/** Get the value of coefficient dE<sub>j,s</sub>/dβ.
*
* @return the coefficient dE<sub>j,s</sub>/dβ
*/
public T getdCoefEdbeta() {
return coefEandDeriv[4];
}
}
/** This class computes the coefficients for the generating function S and its derivatives.
* <p>
* The form of the generating functions is: <br>
* S = C⁰ + Σ<sub>j=1</sub><sup>N+1</sup>(C<sup>j</sup> * cos(jF) + S<sup>j</sup> * sin(jF)) <br>
* The coefficients C⁰, C<sup>j</sup>, S<sup>j</sup> are the Fourrier coefficients
* presented in Danielson 4.2-14,15 except for the case j=1 where
* C¹ = C¹<sub>Fourier</sub> - hU and
* S¹ = S¹<sub>Fourier</sub> + kU <br>
* Also the coefficients of the derivatives of S by a, k, h, α, β, γ and λ
* are computed end expressed in a similar manner. The formulas used are 4.2-19, 20, 23, 24
* </p>
* @author Lucian Barbulescu
*/
private class GeneratingFunctionCoefficients {
/** The Fourier coefficients as presented in Danielson 4.2-14,15. */
private final FourierCjSjCoefficients cjsjFourier;
/** Maximum value of j index. */
private final int jMax;
/** The coefficients C<sup>j</sup> of the function S and its derivatives.
* <p>
* The index j belongs to the interval [0,jMax]. The coefficient C⁰ is the free coefficient.<br>
* Each column of the matrix contains the coefficient corresponding to the following functions: <br/>
* - S <br/>
* - dS / da <br/>
* - dS / dk <br/>
* - dS / dh <br/>
* - dS / dα <br/>
* - dS / dβ <br/>
* - dS / dγ <br/>
* - dS / dλ
* </p>
*/
private final double[][] cjCoefs;
/** The coefficients S<sup>j</sup> of the function S and its derivatives.
* <p>
* The index j belongs to the interval [0,jMax].<br>
* Each column of the matrix contains the coefficient corresponding to the following functions: <br/>
* - S <br/>
* - dS / da <br/>
* - dS / dk <br/>
* - dS / dh <br/>
* - dS / dα <br/>
* - dS / dβ <br/>
* - dS / dγ <br/>
* - dS / dλ
* </p>
*/
private final double[][] sjCoefs;
/**
* Standard constructor.
*
* @param nMax maximum value of n index
* @param sMax maximum value of s index
* @param jMax maximum value of j index
* @param context container for attributes
* @param hansen hansen objects
* @param aoR3Pow a / R3 up to power maxAR3Pow
* @param qns Qns coefficients
*/
GeneratingFunctionCoefficients(final int nMax, final int sMax, final int jMax,
final DSSTThirdBodyDynamicContext context,
final HansenObjects hansen,
final double[] aoR3Pow, final double[][] qns) {
this.jMax = jMax;
this.cjsjFourier = new FourierCjSjCoefficients(nMax, sMax, jMax, context, aoR3Pow, qns);
this.cjCoefs = new double[8][jMax + 1];
this.sjCoefs = new double[8][jMax + 1];
computeGeneratingFunctionCoefficients(context, hansen, aoR3Pow, qns);
}
/**
* Compute the coefficients for the generating function S and its derivatives.
* @param context container for attributes
* @param hansenObjects hansen objects
* @param aoR3Pow a / R3 up to power maxAR3Pow
* @param qns Qns coefficients
*/
private void computeGeneratingFunctionCoefficients(final DSSTThirdBodyDynamicContext context, final HansenObjects hansenObjects,
final double[] aoR3Pow, final double[][] qns) {
final AuxiliaryElements auxiliaryElements = context.getAuxiliaryElements();
// Access to potential U derivatives
final UAnddU udu = new UAnddU(context, hansenObjects, aoR3Pow, qns);
//Compute the C<sup>j</sup> coefficients
for (int j = 1; j <= jMax; j++) {
//Compute the C<sup>j</sup> coefficients
cjCoefs[0][j] = cjsjFourier.getCj(j);
cjCoefs[1][j] = cjsjFourier.getdCjda(j);
cjCoefs[2][j] = cjsjFourier.getdCjdk(j) - (cjsjFourier.getSjLambda(j - 1) - cjsjFourier.getSjLambda(j + 1)) / 2;
cjCoefs[3][j] = cjsjFourier.getdCjdh(j) - (cjsjFourier.getCjLambda(j - 1) + cjsjFourier.getCjLambda(j + 1)) / 2;
cjCoefs[4][j] = cjsjFourier.getdCjdalpha(j);
cjCoefs[5][j] = cjsjFourier.getdCjdbeta(j);
cjCoefs[6][j] = cjsjFourier.getdCjdgamma(j);
cjCoefs[7][j] = cjsjFourier.getCjLambda(j);
//Compute the S<sup>j</sup> coefficients
sjCoefs[0][j] = cjsjFourier.getSj(j);
sjCoefs[1][j] = cjsjFourier.getdSjda(j);
sjCoefs[2][j] = cjsjFourier.getdSjdk(j) + (cjsjFourier.getCjLambda(j - 1) - cjsjFourier.getCjLambda(j + 1)) / 2;
sjCoefs[3][j] = cjsjFourier.getdSjdh(j) - (cjsjFourier.getSjLambda(j - 1) + cjsjFourier.getSjLambda(j + 1)) / 2;
sjCoefs[4][j] = cjsjFourier.getdSjdalpha(j);
sjCoefs[5][j] = cjsjFourier.getdSjdbeta(j);
sjCoefs[6][j] = cjsjFourier.getdSjdgamma(j);
sjCoefs[7][j] = cjsjFourier.getSjLambda(j);
//In the special case j == 1 there are some additional terms to be added
if (j == 1) {
//Additional terms for C<sup>j</sup> coefficients
cjCoefs[0][j] += -auxiliaryElements.getH() * udu.getU();
cjCoefs[1][j] += -auxiliaryElements.getH() * udu.getdUda();
cjCoefs[2][j] += -auxiliaryElements.getH() * udu.getdUdk();
cjCoefs[3][j] += -(auxiliaryElements.getH() * udu.getdUdh() + udu.getU() + cjsjFourier.getC0Lambda());
cjCoefs[4][j] += -auxiliaryElements.getH() * udu.getdUdAl();
cjCoefs[5][j] += -auxiliaryElements.getH() * udu.getdUdBe();
cjCoefs[6][j] += -auxiliaryElements.getH() * udu.getdUdGa();
//Additional terms for S<sup>j</sup> coefficients
sjCoefs[0][j] += auxiliaryElements.getK() * udu.getU();
sjCoefs[1][j] += auxiliaryElements.getK() * udu.getdUda();
sjCoefs[2][j] += auxiliaryElements.getK() * udu.getdUdk() + udu.getU() + cjsjFourier.getC0Lambda();
sjCoefs[3][j] += auxiliaryElements.getK() * udu.getdUdh();
sjCoefs[4][j] += auxiliaryElements.getK() * udu.getdUdAl();
sjCoefs[5][j] += auxiliaryElements.getK() * udu.getdUdBe();
sjCoefs[6][j] += auxiliaryElements.getK() * udu.getdUdGa();
}
}
}
/** Get the coefficient C<sup>j</sup> for the function S.
* <br>
* Possible values for j are within the interval [0,jMax].
* The value 0 is used to obtain the free coefficient C⁰
* @param j j index
* @return C<sup>j</sup> for the function S
*/
public double getSCj(final int j) {
return cjCoefs[0][j];
}
/** Get the coefficient S<sup>j</sup> for the function S.
* <br>
* Possible values for j are within the interval [1,jMax].
* @param j j index
* @return S<sup>j</sup> for the function S
*/
public double getSSj(final int j) {
return sjCoefs[0][j];
}
/** Get the coefficient C<sup>j</sup> for the derivative dS/da.
* <br>
* Possible values for j are within the interval [0,jMax].
* The value 0 is used to obtain the free coefficient C⁰
* @param j j index
* @return C<sup>j</sup> for the function dS/da
*/
public double getdSdaCj(final int j) {
return cjCoefs[1][j];
}
/** Get the coefficient S<sup>j</sup> for the derivative dS/da.
* <br>
* Possible values for j are within the interval [1,jMax].
* @param j j index
* @return S<sup>j</sup> for the derivative dS/da
*/
public double getdSdaSj(final int j) {
return sjCoefs[1][j];
}
/** Get the coefficient C<sup>j</sup> for the derivative dS/dk
* <br>
* Possible values for j are within the interval [0,jMax].
* The value 0 is used to obtain the free coefficient C⁰
* @param j j index
* @return C<sup>j</sup> for the function dS/dk
*/
public double getdSdkCj(final int j) {
return cjCoefs[2][j];
}
/** Get the coefficient S<sup>j</sup> for the derivative dS/dk.
* <br>
* Possible values for j are within the interval [1,jMax].
* @param j j index
* @return S<sup>j</sup> for the derivative dS/dk
*/
public double getdSdkSj(final int j) {
return sjCoefs[2][j];
}
/** Get the coefficient C<sup>j</sup> for the derivative dS/dh
* <br>
* Possible values for j are within the interval [0,jMax].
* The value 0 is used to obtain the free coefficient C⁰
* @param j j index
* @return C<sup>j</sup> for the function dS/dh
*/
public double getdSdhCj(final int j) {
return cjCoefs[3][j];
}
/** Get the coefficient S<sup>j</sup> for the derivative dS/dh.
* <br>
* Possible values for j are within the interval [1,jMax].
* @param j j index
* @return S<sup>j</sup> for the derivative dS/dh
*/
public double getdSdhSj(final int j) {
return sjCoefs[3][j];
}
/** Get the coefficient C<sup>j</sup> for the derivative dS/dα
* <br>
* Possible values for j are within the interval [0,jMax].
* The value 0 is used to obtain the free coefficient C⁰
* @param j j index
* @return C<sup>j</sup> for the function dS/dα
*/
public double getdSdalphaCj(final int j) {
return cjCoefs[4][j];
}
/** Get the coefficient S<sup>j</sup> for the derivative dS/dα.
* <br>
* Possible values for j are within the interval [1,jMax].
* @param j j index
* @return S<sup>j</sup> for the derivative dS/dα
*/
public double getdSdalphaSj(final int j) {
return sjCoefs[4][j];
}
/** Get the coefficient C<sup>j</sup> for the derivative dS/dβ
* <br>
* Possible values for j are within the interval [0,jMax].
* The value 0 is used to obtain the free coefficient C⁰
* @param j j index
* @return C<sup>j</sup> for the function dS/dβ
*/
public double getdSdbetaCj(final int j) {
return cjCoefs[5][j];
}
/** Get the coefficient S<sup>j</sup> for the derivative dS/dβ.
* <br>
* Possible values for j are within the interval [1,jMax].
* @param j j index
* @return S<sup>j</sup> for the derivative dS/dβ
*/
public double getdSdbetaSj(final int j) {
return sjCoefs[5][j];
}
/** Get the coefficient C<sup>j</sup> for the derivative dS/dγ
* <br>
* Possible values for j are within the interval [0,jMax].
* The value 0 is used to obtain the free coefficient C⁰
* @param j j index
* @return C<sup>j</sup> for the function dS/dγ
*/
public double getdSdgammaCj(final int j) {
return cjCoefs[6][j];
}
/** Get the coefficient S<sup>j</sup> for the derivative dS/dγ.
* <br>
* Possible values for j are within the interval [1,jMax].
* @param j j index
* @return S<sup>j</sup> for the derivative dS/dγ
*/
public double getdSdgammaSj(final int j) {
return sjCoefs[6][j];
}
/** Get the coefficient C<sup>j</sup> for the derivative dS/dλ
* <br>
* Possible values for j are within the interval [0,jMax].
* The value 0 is used to obtain the free coefficient C⁰
* @param j j index
* @return C<sup>j</sup> for the function dS/dλ
*/
public double getdSdlambdaCj(final int j) {
return cjCoefs[7][j];
}
/** Get the coefficient S<sup>j</sup> for the derivative dS/dλ.
* <br>
* Possible values for j are within the interval [1,jMax].
* @param j j index
* @return S<sup>j</sup> for the derivative dS/dλ
*/
public double getdSdlambdaSj(final int j) {
return sjCoefs[7][j];
}
}
/** This class computes the coefficients for the generating function S and its derivatives.
* <p>
* The form of the generating functions is: <br>
* S = C⁰ + Σ<sub>j=1</sub><sup>N+1</sup>(C<sup>j</sup> * cos(jF) + S<sup>j</sup> * sin(jF)) <br>
* The coefficients C⁰, C<sup>j</sup>, S<sup>j</sup> are the Fourrier coefficients
* presented in Danielson 4.2-14,15 except for the case j=1 where
* C¹ = C¹<sub>Fourier</sub> - hU and
* S¹ = S¹<sub>Fourier</sub> + kU <br>
* Also the coefficients of the derivatives of S by a, k, h, α, β, γ and λ
* are computed end expressed in a similar manner. The formulas used are 4.2-19, 20, 23, 24
* </p>
* @author Lucian Barbulescu
*/
private class FieldGeneratingFunctionCoefficients <T extends CalculusFieldElement<T>> {
/** The Fourier coefficients as presented in Danielson 4.2-14,15. */
private final FieldFourierCjSjCoefficients<T> cjsjFourier;
/** Maximum value of j index. */
private final int jMax;
/** The coefficients C<sup>j</sup> of the function S and its derivatives.
* <p>
* The index j belongs to the interval [0,jMax]. The coefficient C⁰ is the free coefficient.<br>
* Each column of the matrix contains the coefficient corresponding to the following functions: <br/>
* - S <br/>
* - dS / da <br/>
* - dS / dk <br/>
* - dS / dh <br/>
* - dS / dα <br/>
* - dS / dβ <br/>
* - dS / dγ <br/>
* - dS / dλ
* </p>
*/
private final T[][] cjCoefs;
/** The coefficients S<sup>j</sup> of the function S and its derivatives.
* <p>
* The index j belongs to the interval [0,jMax].<br>
* Each column of the matrix contains the coefficient corresponding to the following functions: <br/>
* - S <br/>
* - dS / da <br/>
* - dS / dk <br/>
* - dS / dh <br/>
* - dS / dα <br/>
* - dS / dβ <br/>
* - dS / dγ <br/>
* - dS / dλ
* </p>
*/
private final T[][] sjCoefs;
/**
* Standard constructor.
*
* @param nMax maximum value of n index
* @param sMax maximum value of s index
* @param jMax maximum value of j index
* @param context container for attributes
* @param hansen hansen objects
* @param field field used by default
* @param aoR3Pow a / R3 up to power maxAR3Pow
* @param qns Qns coefficients
*/
FieldGeneratingFunctionCoefficients(final int nMax, final int sMax, final int jMax,
final FieldDSSTThirdBodyDynamicContext<T> context,
final FieldHansenObjects<T> hansen, final Field<T> field,
final T[] aoR3Pow, final T[][] qns) {
this.jMax = jMax;
this.cjsjFourier = new FieldFourierCjSjCoefficients<>(nMax, sMax, jMax, context, aoR3Pow, qns, field);
this.cjCoefs = MathArrays.buildArray(field, 8, jMax + 1);
this.sjCoefs = MathArrays.buildArray(field, 8, jMax + 1);
computeGeneratingFunctionCoefficients(context, hansen, aoR3Pow, qns);
}
/**
* Compute the coefficients for the generating function S and its derivatives.
* @param context container for attributes
* @param hansenObjects hansen objects
* @param aoR3Pow a / R3 up to power maxAR3Pow
* @param qns Qns coefficients
*/
private void computeGeneratingFunctionCoefficients(final FieldDSSTThirdBodyDynamicContext<T> context,
final FieldHansenObjects<T> hansenObjects,
final T[] aoR3Pow, final T[][] qns) {
final FieldAuxiliaryElements<T> auxiliaryElements = context.getFieldAuxiliaryElements();
// Access to potential U derivatives
final FieldUAnddU<T> udu = new FieldUAnddU<>(context, hansenObjects, aoR3Pow, qns);
//Compute the C<sup>j</sup> coefficients
for (int j = 1; j <= jMax; j++) {
//Compute the C<sup>j</sup> coefficients
cjCoefs[0][j] = cjsjFourier.getCj(j);
cjCoefs[1][j] = cjsjFourier.getdCjda(j);
cjCoefs[2][j] = cjsjFourier.getdCjdk(j).subtract((cjsjFourier.getSjLambda(j - 1).subtract(cjsjFourier.getSjLambda(j + 1))).divide(2.));
cjCoefs[3][j] = cjsjFourier.getdCjdh(j).subtract((cjsjFourier.getCjLambda(j - 1).add(cjsjFourier.getCjLambda(j + 1))).divide(2.));
cjCoefs[4][j] = cjsjFourier.getdCjdalpha(j);
cjCoefs[5][j] = cjsjFourier.getdCjdbeta(j);
cjCoefs[6][j] = cjsjFourier.getdCjdgamma(j);
cjCoefs[7][j] = cjsjFourier.getCjLambda(j);
//Compute the S<sup>j</sup> coefficients
sjCoefs[0][j] = cjsjFourier.getSj(j);
sjCoefs[1][j] = cjsjFourier.getdSjda(j);
sjCoefs[2][j] = cjsjFourier.getdSjdk(j).add((cjsjFourier.getCjLambda(j - 1).subtract(cjsjFourier.getCjLambda(j + 1))).divide(2.));
sjCoefs[3][j] = cjsjFourier.getdSjdh(j).subtract((cjsjFourier.getSjLambda(j - 1).add(cjsjFourier.getSjLambda(j + 1))).divide(2.));
sjCoefs[4][j] = cjsjFourier.getdSjdalpha(j);
sjCoefs[5][j] = cjsjFourier.getdSjdbeta(j);
sjCoefs[6][j] = cjsjFourier.getdSjdgamma(j);
sjCoefs[7][j] = cjsjFourier.getSjLambda(j);
//In the special case j == 1 there are some additional terms to be added
if (j == 1) {
//Additional terms for C<sup>j</sup> coefficients
cjCoefs[0][j] = cjCoefs[0][j].add(auxiliaryElements.getH().negate().multiply(udu.getU()));
cjCoefs[1][j] = cjCoefs[1][j].add(auxiliaryElements.getH().negate().multiply(udu.getdUda()));
cjCoefs[2][j] = cjCoefs[2][j].add(auxiliaryElements.getH().negate().multiply(udu.getdUdk()));
cjCoefs[3][j] = cjCoefs[3][j].add(auxiliaryElements.getH().multiply(udu.getdUdh()).add(udu.getU()).add(cjsjFourier.getC0Lambda()).negate());
cjCoefs[4][j] = cjCoefs[4][j].add(auxiliaryElements.getH().negate().multiply(udu.getdUdAl()));
cjCoefs[5][j] = cjCoefs[5][j].add(auxiliaryElements.getH().negate().multiply(udu.getdUdBe()));
cjCoefs[6][j] = cjCoefs[6][j].add(auxiliaryElements.getH().negate().multiply(udu.getdUdGa()));
//Additional terms for S<sup>j</sup> coefficients
sjCoefs[0][j] = sjCoefs[0][j].add(auxiliaryElements.getK().multiply(udu.getU()));
sjCoefs[1][j] = sjCoefs[1][j].add(auxiliaryElements.getK().multiply(udu.getdUda()));
sjCoefs[2][j] = sjCoefs[2][j].add(auxiliaryElements.getK().multiply(udu.getdUdk()).add(udu.getU()).add(cjsjFourier.getC0Lambda()));
sjCoefs[3][j] = sjCoefs[3][j].add(auxiliaryElements.getK().multiply(udu.getdUdh()));
sjCoefs[4][j] = sjCoefs[4][j].add(auxiliaryElements.getK().multiply(udu.getdUdAl()));
sjCoefs[5][j] = sjCoefs[5][j].add(auxiliaryElements.getK().multiply(udu.getdUdBe()));
sjCoefs[6][j] = sjCoefs[6][j].add(auxiliaryElements.getK().multiply(udu.getdUdGa()));
}
}
}
/** Get the coefficient C<sup>j</sup> for the function S.
* <br>
* Possible values for j are within the interval [0,jMax].
* The value 0 is used to obtain the free coefficient C⁰
* @param j j index
* @return C<sup>j</sup> for the function S
*/
public T getSCj(final int j) {
return cjCoefs[0][j];
}
/** Get the coefficient S<sup>j</sup> for the function S.
* <br>
* Possible values for j are within the interval [1,jMax].
* @param j j index
* @return S<sup>j</sup> for the function S
*/
public T getSSj(final int j) {
return sjCoefs[0][j];
}
/** Get the coefficient C<sup>j</sup> for the derivative dS/da.
* <br>
* Possible values for j are within the interval [0,jMax].
* The value 0 is used to obtain the free coefficient C⁰
* @param j j index
* @return C<sup>j</sup> for the function dS/da
*/
public T getdSdaCj(final int j) {
return cjCoefs[1][j];
}
/** Get the coefficient S<sup>j</sup> for the derivative dS/da.
* <br>
* Possible values for j are within the interval [1,jMax].
* @param j j index
* @return S<sup>j</sup> for the derivative dS/da
*/
public T getdSdaSj(final int j) {
return sjCoefs[1][j];
}
/** Get the coefficient C<sup>j</sup> for the derivative dS/dk
* <br>
* Possible values for j are within the interval [0,jMax].
* The value 0 is used to obtain the free coefficient C⁰
* @param j j index
* @return C<sup>j</sup> for the function dS/dk
*/
public T getdSdkCj(final int j) {
return cjCoefs[2][j];
}
/** Get the coefficient S<sup>j</sup> for the derivative dS/dk.
* <br>
* Possible values for j are within the interval [1,jMax].
* @param j j index
* @return S<sup>j</sup> for the derivative dS/dk
*/
public T getdSdkSj(final int j) {
return sjCoefs[2][j];
}
/** Get the coefficient C<sup>j</sup> for the derivative dS/dh
* <br>
* Possible values for j are within the interval [0,jMax].
* The value 0 is used to obtain the free coefficient C⁰
* @param j j index
* @return C<sup>j</sup> for the function dS/dh
*/
public T getdSdhCj(final int j) {
return cjCoefs[3][j];
}
/** Get the coefficient S<sup>j</sup> for the derivative dS/dh.
* <br>
* Possible values for j are within the interval [1,jMax].
* @param j j index
* @return S<sup>j</sup> for the derivative dS/dh
*/
public T getdSdhSj(final int j) {
return sjCoefs[3][j];
}
/** Get the coefficient C<sup>j</sup> for the derivative dS/dα
* <br>
* Possible values for j are within the interval [0,jMax].
* The value 0 is used to obtain the free coefficient C⁰
* @param j j index
* @return C<sup>j</sup> for the function dS/dα
*/
public T getdSdalphaCj(final int j) {
return cjCoefs[4][j];
}
/** Get the coefficient S<sup>j</sup> for the derivative dS/dα.
* <br>
* Possible values for j are within the interval [1,jMax].
* @param j j index
* @return S<sup>j</sup> for the derivative dS/dα
*/
public T getdSdalphaSj(final int j) {
return sjCoefs[4][j];
}
/** Get the coefficient C<sup>j</sup> for the derivative dS/dβ
* <br>
* Possible values for j are within the interval [0,jMax].
* The value 0 is used to obtain the free coefficient C⁰
* @param j j index
* @return C<sup>j</sup> for the function dS/dβ
*/
public T getdSdbetaCj(final int j) {
return cjCoefs[5][j];
}
/** Get the coefficient S<sup>j</sup> for the derivative dS/dβ.
* <br>
* Possible values for j are within the interval [1,jMax].
* @param j j index
* @return S<sup>j</sup> for the derivative dS/dβ
*/
public T getdSdbetaSj(final int j) {
return sjCoefs[5][j];
}
/** Get the coefficient C<sup>j</sup> for the derivative dS/dγ
* <br>
* Possible values for j are within the interval [0,jMax].
* The value 0 is used to obtain the free coefficient C⁰
* @param j j index
* @return C<sup>j</sup> for the function dS/dγ
*/
public T getdSdgammaCj(final int j) {
return cjCoefs[6][j];
}
/** Get the coefficient S<sup>j</sup> for the derivative dS/dγ.
* <br>
* Possible values for j are within the interval [1,jMax].
* @param j j index
* @return S<sup>j</sup> for the derivative dS/dγ
*/
public T getdSdgammaSj(final int j) {
return sjCoefs[6][j];
}
/** Get the coefficient C<sup>j</sup> for the derivative dS/dλ
* <br>
* Possible values for j are within the interval [0,jMax].
* The value 0 is used to obtain the free coefficient C⁰
* @param j j index
* @return C<sup>j</sup> for the function dS/dλ
*/
public T getdSdlambdaCj(final int j) {
return cjCoefs[7][j];
}
/** Get the coefficient S<sup>j</sup> for the derivative dS/dλ.
* <br>
* Possible values for j are within the interval [1,jMax].
* @param j j index
* @return S<sup>j</sup> for the derivative dS/dλ
*/
public T getdSdlambdaSj(final int j) {
return sjCoefs[7][j];
}
}
/**
* The coefficients used to compute the short periodic contribution for the Third body perturbation.
* <p>
* The short periodic contribution for the Third Body is expressed in Danielson 4.2-25.<br>
* The coefficients C<sub>i</sub>⁰, C<sub>i</sub><sup>j</sup>, S<sub>i</sub><sup>j</sup>
* are computed by replacing the corresponding values in formula 2.5.5-10.
* </p>
* @author Lucian Barbulescu
*/
private static class ThirdBodyShortPeriodicCoefficients implements ShortPeriodTerms {
/** Maximal value for j. */
private final int jMax;
/** Number of points used in the interpolation process. */
private final int interpolationPoints;
/** Max frequency of F. */
private final int maxFreqF;
/** Coefficients prefix. */
private final String prefix;
/** All coefficients slots. */
private final transient TimeSpanMap<Slot> slots;
/**
* Standard constructor.
* @param interpolationPoints number of points used in the interpolation process
* @param jMax maximal value for j
* @param maxFreqF Max frequency of F
* @param bodyName third body name
* @param slots all coefficients slots
*/
ThirdBodyShortPeriodicCoefficients(final int jMax, final int interpolationPoints,
final int maxFreqF, final String bodyName,
final TimeSpanMap<Slot> slots) {
this.jMax = jMax;
this.interpolationPoints = interpolationPoints;
this.maxFreqF = maxFreqF;
this.prefix = DSSTThirdBody.SHORT_PERIOD_PREFIX + bodyName + "-";
this.slots = slots;
}
/** Get the slot valid for some date.
* @param meanStates mean states defining the slot
* @return slot valid at the specified date
*/
public Slot createSlot(final SpacecraftState... meanStates) {
final Slot slot = new Slot(jMax, interpolationPoints);
final AbsoluteDate first = meanStates[0].getDate();
final AbsoluteDate last = meanStates[meanStates.length - 1].getDate();
final int compare = first.compareTo(last);
if (compare < 0) {
slots.addValidAfter(slot, first, false);
} else if (compare > 0) {
slots.addValidBefore(slot, first, false);
} else {
// single date, valid for all time
slots.addValidAfter(slot, AbsoluteDate.PAST_INFINITY, false);
}
return slot;
}
/** {@inheritDoc} */
@Override
public double[] value(final Orbit meanOrbit) {
// select the coefficients slot
final Slot slot = slots.get(meanOrbit.getDate());
// the current eccentric longitude
final double F = meanOrbit.getLE();
//initialize the short periodic contribution with the corresponding C⁰ coeficient
final double[] shortPeriodic = slot.cij[0].value(meanOrbit.getDate());
// Add the cos and sin dependent terms
for (int j = 1; j <= maxFreqF; j++) {
//compute cos and sin
final SinCos scjF = FastMath.sinCos(j * F);
final double[] c = slot.cij[j].value(meanOrbit.getDate());
final double[] s = slot.sij[j].value(meanOrbit.getDate());
for (int i = 0; i < 6; i++) {
shortPeriodic[i] += c[i] * scjF.cos() + s[i] * scjF.sin();
}
}
return shortPeriodic;
}
/** {@inheritDoc} */
@Override
public String getCoefficientsKeyPrefix() {
return prefix;
}
/** {@inheritDoc}
* <p>
* For third body attraction forces,there are maxFreqF + 1 cj coefficients,
* maxFreqF sj coefficients where maxFreqF depends on the orbit.
* The j index is the integer multiplier for the eccentric longitude argument
* in the cj and sj coefficients.
* </p>
*/
@Override
public Map<String, double[]> getCoefficients(final AbsoluteDate date, final Set<String> selected) {
// select the coefficients slot
final Slot slot = slots.get(date);
final Map<String, double[]> coefficients = new HashMap<>(2 * maxFreqF + 1);
storeIfSelected(coefficients, selected, slot.cij[0].value(date), "c", 0);
for (int j = 1; j <= maxFreqF; j++) {
storeIfSelected(coefficients, selected, slot.cij[j].value(date), "c", j);
storeIfSelected(coefficients, selected, slot.sij[j].value(date), "s", j);
}
return coefficients;
}
/** Put a coefficient in a map if selected.
* @param map map to populate
* @param selected set of coefficients that should be put in the map
* (empty set means all coefficients are selected)
* @param value coefficient value
* @param id coefficient identifier
* @param indices list of coefficient indices
*/
private void storeIfSelected(final Map<String, double[]> map, final Set<String> selected,
final double[] value, final String id, final int... indices) {
final StringBuilder keyBuilder = new StringBuilder(getCoefficientsKeyPrefix());
keyBuilder.append(id);
for (int index : indices) {
keyBuilder.append('[').append(index).append(']');
}
final String key = keyBuilder.toString();
if (selected.isEmpty() || selected.contains(key)) {
map.put(key, value);
}
}
}
/**
* The coefficients used to compute the short periodic contribution for the Third body perturbation.
* <p>
* The short periodic contribution for the Third Body is expressed in Danielson 4.2-25.<br>
* The coefficients C<sub>i</sub>⁰, C<sub>i</sub><sup>j</sup>, S<sub>i</sub><sup>j</sup>
* are computed by replacing the corresponding values in formula 2.5.5-10.
* </p>
* @author Lucian Barbulescu
*/
private static class FieldThirdBodyShortPeriodicCoefficients <T extends CalculusFieldElement<T>> implements FieldShortPeriodTerms<T> {
/** Maximal value for j. */
private final int jMax;
/** Number of points used in the interpolation process. */
private final int interpolationPoints;
/** Max frequency of F. */
private final int maxFreqF;
/** Coefficients prefix. */
private final String prefix;
/** All coefficients slots. */
private final transient FieldTimeSpanMap<FieldSlot<T>, T> slots;
/**
* Standard constructor.
* @param interpolationPoints number of points used in the interpolation process
* @param jMax maximal value for j
* @param maxFreqF Max frequency of F
* @param bodyName third body name
* @param slots all coefficients slots
*/
FieldThirdBodyShortPeriodicCoefficients(final int jMax, final int interpolationPoints,
final int maxFreqF, final String bodyName,
final FieldTimeSpanMap<FieldSlot<T>, T> slots) {
this.jMax = jMax;
this.interpolationPoints = interpolationPoints;
this.maxFreqF = maxFreqF;
this.prefix = DSSTThirdBody.SHORT_PERIOD_PREFIX + bodyName + "-";
this.slots = slots;
}
/** Get the slot valid for some date.
* @param meanStates mean states defining the slot
* @return slot valid at the specified date
*/
@SuppressWarnings("unchecked")
public FieldSlot<T> createSlot(final FieldSpacecraftState<T>... meanStates) {
final FieldSlot<T> slot = new FieldSlot<>(jMax, interpolationPoints);
final FieldAbsoluteDate<T> first = meanStates[0].getDate();
final FieldAbsoluteDate<T> last = meanStates[meanStates.length - 1].getDate();
if (first.compareTo(last) <= 0) {
slots.addValidAfter(slot, first);
} else {
slots.addValidBefore(slot, first);
}
return slot;
}
/** {@inheritDoc} */
@Override
public T[] value(final FieldOrbit<T> meanOrbit) {
// select the coefficients slot
final FieldSlot<T> slot = slots.get(meanOrbit.getDate());
// the current eccentric longitude
final T F = meanOrbit.getLE();
//initialize the short periodic contribution with the corresponding C⁰ coeficient
final T[] shortPeriodic = slot.cij[0].value(meanOrbit.getDate());
// Add the cos and sin dependent terms
for (int j = 1; j <= maxFreqF; j++) {
//compute cos and sin
final FieldSinCos<T> scjF = FastMath.sinCos(F.multiply(j));
final T[] c = slot.cij[j].value(meanOrbit.getDate());
final T[] s = slot.sij[j].value(meanOrbit.getDate());
for (int i = 0; i < 6; i++) {
shortPeriodic[i] = shortPeriodic[i].add(c[i].multiply(scjF.cos()).add(s[i].multiply(scjF.sin())));
}
}
return shortPeriodic;
}
/** {@inheritDoc} */
@Override
public String getCoefficientsKeyPrefix() {
return prefix;
}
/** {@inheritDoc}
* <p>
* For third body attraction forces,there are maxFreqF + 1 cj coefficients,
* maxFreqF sj coefficients where maxFreqF depends on the orbit.
* The j index is the integer multiplier for the eccentric longitude argument
* in the cj and sj coefficients.
* </p>
*/
@Override
public Map<String, T[]> getCoefficients(final FieldAbsoluteDate<T> date, final Set<String> selected) {
// select the coefficients slot
final FieldSlot<T> slot = slots.get(date);
final Map<String, T[]> coefficients = new HashMap<>(2 * maxFreqF + 1);
storeIfSelected(coefficients, selected, slot.cij[0].value(date), "c", 0);
for (int j = 1; j <= maxFreqF; j++) {
storeIfSelected(coefficients, selected, slot.cij[j].value(date), "c", j);
storeIfSelected(coefficients, selected, slot.sij[j].value(date), "s", j);
}
return coefficients;
}
/** Put a coefficient in a map if selected.
* @param map map to populate
* @param selected set of coefficients that should be put in the map
* (empty set means all coefficients are selected)
* @param value coefficient value
* @param id coefficient identifier
* @param indices list of coefficient indices
*/
private void storeIfSelected(final Map<String, T[]> map, final Set<String> selected,
final T[] value, final String id, final int... indices) {
final StringBuilder keyBuilder = new StringBuilder(getCoefficientsKeyPrefix());
keyBuilder.append(id);
for (int index : indices) {
keyBuilder.append('[').append(index).append(']');
}
final String key = keyBuilder.toString();
if (selected.isEmpty() || selected.contains(key)) {
map.put(key, value);
}
}
}
/** Coefficients valid for one time slot. */
private static class Slot {
/** The coefficients C<sub>i</sub><sup>j</sup>.
* <p>
* The index order is cij[j][i] <br/>
* i corresponds to the equinoctial element, as follows: <br/>
* - i=0 for a <br/>
* - i=1 for k <br/>
* - i=2 for h <br/>
* - i=3 for q <br/>
* - i=4 for p <br/>
* - i=5 for λ <br/>
* </p>
*/
private final ShortPeriodicsInterpolatedCoefficient[] cij;
/** The coefficients S<sub>i</sub><sup>j</sup>.
* <p>
* The index order is sij[j][i] <br/>
* i corresponds to the equinoctial element, as follows: <br/>
* - i=0 for a <br/>
* - i=1 for k <br/>
* - i=2 for h <br/>
* - i=3 for q <br/>
* - i=4 for p <br/>
* - i=5 for λ <br/>
* </p>
*/
private final ShortPeriodicsInterpolatedCoefficient[] sij;
/** Simple constructor.
* @param jMax maximum value for j index
* @param interpolationPoints number of points used in the interpolation process
*/
Slot(final int jMax, final int interpolationPoints) {
// allocate the coefficients arrays
cij = new ShortPeriodicsInterpolatedCoefficient[jMax + 1];
sij = new ShortPeriodicsInterpolatedCoefficient[jMax + 1];
for (int j = 0; j <= jMax; j++) {
cij[j] = new ShortPeriodicsInterpolatedCoefficient(interpolationPoints);
sij[j] = new ShortPeriodicsInterpolatedCoefficient(interpolationPoints);
}
}
}
/** Coefficients valid for one time slot. */
private static class FieldSlot <T extends CalculusFieldElement<T>> {
/** The coefficients C<sub>i</sub><sup>j</sup>.
* <p>
* The index order is cij[j][i] <br/>
* i corresponds to the equinoctial element, as follows: <br/>
* - i=0 for a <br/>
* - i=1 for k <br/>
* - i=2 for h <br/>
* - i=3 for q <br/>
* - i=4 for p <br/>
* - i=5 for λ <br/>
* </p>
*/
private final FieldShortPeriodicsInterpolatedCoefficient<T>[] cij;
/** The coefficients S<sub>i</sub><sup>j</sup>.
* <p>
* The index order is sij[j][i] <br/>
* i corresponds to the equinoctial element, as follows: <br/>
* - i=0 for a <br/>
* - i=1 for k <br/>
* - i=2 for h <br/>
* - i=3 for q <br/>
* - i=4 for p <br/>
* - i=5 for λ <br/>
* </p>
*/
private final FieldShortPeriodicsInterpolatedCoefficient<T>[] sij;
/** Simple constructor.
* @param jMax maximum value for j index
* @param interpolationPoints number of points used in the interpolation process
*/
@SuppressWarnings("unchecked")
FieldSlot(final int jMax, final int interpolationPoints) {
// allocate the coefficients arrays
cij = (FieldShortPeriodicsInterpolatedCoefficient<T>[]) Array.newInstance(FieldShortPeriodicsInterpolatedCoefficient.class, jMax + 1);
sij = (FieldShortPeriodicsInterpolatedCoefficient<T>[]) Array.newInstance(FieldShortPeriodicsInterpolatedCoefficient.class, jMax + 1);
for (int j = 0; j <= jMax; j++) {
cij[j] = new FieldShortPeriodicsInterpolatedCoefficient<>(interpolationPoints);
sij[j] = new FieldShortPeriodicsInterpolatedCoefficient<>(interpolationPoints);
}
}
}
/** Compute potential and potential derivatives with respect to orbital parameters. */
private class UAnddU {
/** The current value of the U function. <br/>
* Needed for the short periodic contribution */
private double U;
/** dU / da. */
private double dUda;
/** dU / dk. */
private double dUdk;
/** dU / dh. */
private double dUdh;
/** dU / dAlpha. */
private double dUdAl;
/** dU / dBeta. */
private double dUdBe;
/** dU / dGamma. */
private double dUdGa;
/** Simple constuctor.
* @param context container for attributes
* @param hansen hansen objects
* @param aoR3Pow a / R3 up to power maxAR3Pow
* @param qns Qns coefficients
*/
UAnddU(final DSSTThirdBodyDynamicContext context, final HansenObjects hansen,
final double[] aoR3Pow, final double[][] qns) {
// Auxiliary elements related to the current orbit
final AuxiliaryElements auxiliaryElements = context.getAuxiliaryElements();
// Gs and Hs coefficients
final double[][] GsHs = CoefficientsFactory.computeGsHs(auxiliaryElements.getK(), auxiliaryElements.getH(), context.getAlpha(), context.getBeta(), staticContext.getMaxEccPow());
// Initialise U.
U = 0.;
// Potential derivatives
dUda = 0.;
dUdk = 0.;
dUdh = 0.;
dUdAl = 0.;
dUdBe = 0.;
dUdGa = 0.;
for (int s = 0; s <= staticContext.getMaxEccPow(); s++) {
// initialise the Hansen roots
hansen.computeHansenObjectsInitValues(context, auxiliaryElements.getB(), s);
// Get the current Gs coefficient
final double gs = GsHs[0][s];
// Compute Gs partial derivatives from 3.1-(9)
double dGsdh = 0.;
double dGsdk = 0.;
double dGsdAl = 0.;
double dGsdBe = 0.;
if (s > 0) {
// First get the G(s-1) and the H(s-1) coefficients
final double sxGsm1 = s * GsHs[0][s - 1];
final double sxHsm1 = s * GsHs[1][s - 1];
// Then compute derivatives
dGsdh = context.getBeta() * sxGsm1 - context.getAlpha() * sxHsm1;
dGsdk = context.getAlpha() * sxGsm1 + context.getBeta() * sxHsm1;
dGsdAl = auxiliaryElements.getK() * sxGsm1 - auxiliaryElements.getH() * sxHsm1;
dGsdBe = auxiliaryElements.getH() * sxGsm1 + auxiliaryElements.getK() * sxHsm1;
}
// Kronecker symbol (2 - delta(0,s))
final double delta0s = (s == 0) ? 1. : 2.;
for (int n = FastMath.max(2, s); n <= staticContext.getMaxAR3Pow(); n++) {
// (n - s) must be even
if ((n - s) % 2 == 0) {
// Extract data from previous computation :
final double kns = hansen.getHansenObjects()[s].getValue(n, auxiliaryElements.getB());
final double dkns = hansen.getHansenObjects()[s].getDerivative(n, auxiliaryElements.getB());
final double vns = Vns.get(new NSKey(n, s));
final double coef0 = delta0s * aoR3Pow[n] * vns;
final double coef1 = coef0 * qns[n][s];
final double coef2 = coef1 * kns;
// dQns/dGamma = Q(n, s + 1) from Equation 3.1-(8)
// for n = s, Q(n, n + 1) = 0. (Cefola & Broucke, 1975)
final double dqns = (n == s) ? 0. : qns[n][s + 1];
//Compute U:
U += coef2 * gs;
// Compute dU / da :
dUda += coef2 * n * gs;
// Compute dU / dh
dUdh += coef1 * (kns * dGsdh + context.getHXXX() * gs * dkns);
// Compute dU / dk
dUdk += coef1 * (kns * dGsdk + context.getKXXX() * gs * dkns);
// Compute dU / dAlpha
dUdAl += coef2 * dGsdAl;
// Compute dU / dBeta
dUdBe += coef2 * dGsdBe;
// Compute dU / dGamma
dUdGa += coef0 * kns * dqns * gs;
}
}
}
// multiply by mu3 / R3
this.U = U * context.getMuoR3();
this.dUda = dUda * context.getMuoR3() / auxiliaryElements.getSma();
this.dUdk = dUdk * context.getMuoR3();
this.dUdh = dUdh * context.getMuoR3();
this.dUdAl = dUdAl * context.getMuoR3();
this.dUdBe = dUdBe * context.getMuoR3();
this.dUdGa = dUdGa * context.getMuoR3();
}
/** Return value of U.
* @return U
*/
public double getU() {
return U;
}
/** Return value of dU / da.
* @return dUda
*/
public double getdUda() {
return dUda;
}
/** Return value of dU / dk.
* @return dUdk
*/
public double getdUdk() {
return dUdk;
}
/** Return value of dU / dh.
* @return dUdh
*/
public double getdUdh() {
return dUdh;
}
/** Return value of dU / dAlpha.
* @return dUdAl
*/
public double getdUdAl() {
return dUdAl;
}
/** Return value of dU / dBeta.
* @return dUdBe
*/
public double getdUdBe() {
return dUdBe;
}
/** Return value of dU / dGamma.
* @return dUdGa
*/
public double getdUdGa() {
return dUdGa;
}
}
/** Compute potential and potential derivatives with respect to orbital parameters. */
private class FieldUAnddU <T extends CalculusFieldElement<T>> {
/** The current value of the U function. <br/>
* Needed for the short periodic contribution */
private T U;
/** dU / da. */
private T dUda;
/** dU / dk. */
private T dUdk;
/** dU / dh. */
private T dUdh;
/** dU / dAlpha. */
private T dUdAl;
/** dU / dBeta. */
private T dUdBe;
/** dU / dGamma. */
private T dUdGa;
/** Simple constuctor.
* @param context container for attributes
* @param hansen hansen objects
* @param aoR3Pow a / R3 up to power maxAR3Pow
* @param qns Qns coefficients
*/
FieldUAnddU(final FieldDSSTThirdBodyDynamicContext<T> context, final FieldHansenObjects<T> hansen,
final T[] aoR3Pow, final T[][] qns) {
// Auxiliary elements related to the current orbit
final FieldAuxiliaryElements<T> auxiliaryElements = context.getFieldAuxiliaryElements();
// Field for array building
final Field<T> field = auxiliaryElements.getDate().getField();
// Zero for initialization
final T zero = field.getZero();
// Gs and Hs coefficients
final T[][] GsHs = CoefficientsFactory.computeGsHs(auxiliaryElements.getK(), auxiliaryElements.getH(), context.getAlpha(), context.getBeta(), staticContext.getMaxEccPow(), field);
// Initialise U.
U = zero;
// Potential derivatives
dUda = zero;
dUdk = zero;
dUdh = zero;
dUdAl = zero;
dUdBe = zero;
dUdGa = zero;
for (int s = 0; s <= staticContext.getMaxEccPow(); s++) {
// initialise the Hansen roots
hansen.computeHansenObjectsInitValues(context, auxiliaryElements.getB(), s);
// Get the current Gs coefficient
final T gs = GsHs[0][s];
// Compute Gs partial derivatives from 3.1-(9)
T dGsdh = zero;
T dGsdk = zero;
T dGsdAl = zero;
T dGsdBe = zero;
if (s > 0) {
// First get the G(s-1) and the H(s-1) coefficients
final T sxGsm1 = GsHs[0][s - 1].multiply(s);
final T sxHsm1 = GsHs[1][s - 1].multiply(s);
// Then compute derivatives
dGsdh = sxGsm1.multiply(context.getBeta()).subtract(sxHsm1.multiply(context.getAlpha()));
dGsdk = sxGsm1.multiply(context.getAlpha()).add(sxHsm1.multiply(context.getBeta()));
dGsdAl = sxGsm1.multiply(auxiliaryElements.getK()).subtract(sxHsm1.multiply(auxiliaryElements.getH()));
dGsdBe = sxGsm1.multiply(auxiliaryElements.getH()).add(sxHsm1.multiply(auxiliaryElements.getK()));
}
// Kronecker symbol (2 - delta(0,s))
final T delta0s = zero.newInstance((s == 0) ? 1. : 2.);
for (int n = FastMath.max(2, s); n <= staticContext.getMaxAR3Pow(); n++) {
// (n - s) must be even
if ((n - s) % 2 == 0) {
// Extract data from previous computation :
final T kns = hansen.getHansenObjects()[s].getValue(n, auxiliaryElements.getB());
final T dkns = hansen.getHansenObjects()[s].getDerivative(n, auxiliaryElements.getB());
final double vns = Vns.get(new NSKey(n, s));
final T coef0 = delta0s.multiply(vns).multiply(aoR3Pow[n]);
final T coef1 = coef0.multiply(qns[n][s]);
final T coef2 = coef1.multiply(kns);
// dQns/dGamma = Q(n, s + 1) from Equation 3.1-(8)
// for n = s, Q(n, n + 1) = 0. (Cefola & Broucke, 1975)
final T dqns = (n == s) ? zero : qns[n][s + 1];
//Compute U:
U = U.add(coef2.multiply(gs));
// Compute dU / da :
dUda = dUda.add(coef2.multiply(n).multiply(gs));
// Compute dU / dh
dUdh = dUdh.add(coef1.multiply(dGsdh.multiply(kns).add(context.getHXXX().multiply(gs).multiply(dkns))));
// Compute dU / dk
dUdk = dUdk.add(coef1.multiply(dGsdk.multiply(kns).add(context.getKXXX().multiply(gs).multiply(dkns))));
// Compute dU / dAlpha
dUdAl = dUdAl.add(coef2.multiply(dGsdAl));
// Compute dU / dBeta
dUdBe = dUdBe.add(coef2.multiply(dGsdBe));
// Compute dU / dGamma
dUdGa = dUdGa.add(coef0.multiply(kns).multiply(dqns).multiply(gs));
}
}
}
// multiply by mu3 / R3
this.U = U.multiply(context.getMuoR3());
this.dUda = dUda.multiply(context.getMuoR3().divide(auxiliaryElements.getSma()));
this.dUdk = dUdk.multiply(context.getMuoR3());
this.dUdh = dUdh.multiply(context.getMuoR3());
this.dUdAl = dUdAl.multiply(context.getMuoR3());
this.dUdBe = dUdBe.multiply(context.getMuoR3());
this.dUdGa = dUdGa.multiply(context.getMuoR3());
}
/** Return value of U.
* @return U
*/
public T getU() {
return U;
}
/** Return value of dU / da.
* @return dUda
*/
public T getdUda() {
return dUda;
}
/** Return value of dU / dk.
* @return dUdk
*/
public T getdUdk() {
return dUdk;
}
/** Return value of dU / dh.
* @return dUdh
*/
public T getdUdh() {
return dUdh;
}
/** Return value of dU / dAlpha.
* @return dUdAl
*/
public T getdUdAl() {
return dUdAl;
}
/** Return value of dU / dBeta.
* @return dUdBe
*/
public T getdUdBe() {
return dUdBe;
}
/** Return value of dU / dGamma.
* @return dUdGa
*/
public T getdUdGa() {
return dUdGa;
}
}
/** Computes init values of the Hansen Objects. */
private static class HansenObjects {
/** Max power for summation. */
private static final int MAX_POWER = 22;
/** An array that contains the objects needed to build the Hansen coefficients. <br/>
* The index is s */
private final HansenThirdBodyLinear[] hansenObjects;
/** Simple constructor. */
HansenObjects() {
this.hansenObjects = new HansenThirdBodyLinear[MAX_POWER + 1];
for (int s = 0; s <= MAX_POWER; s++) {
this.hansenObjects[s] = new HansenThirdBodyLinear(MAX_POWER, s);
}
}
/** Compute init values for hansen objects.
* @param context container for attributes
* @param B = sqrt(1 - e²).
* @param element element of the array to compute the init values
*/
public void computeHansenObjectsInitValues(final DSSTThirdBodyDynamicContext context, final double B, final int element) {
hansenObjects[element].computeInitValues(B, context.getBB(), context.getBBB());
}
/** Get the Hansen Objects.
* @return hansenObjects
*/
public HansenThirdBodyLinear[] getHansenObjects() {
return hansenObjects;
}
}
/** Computes init values of the Hansen Objects. */
private static class FieldHansenObjects<T extends CalculusFieldElement<T>> {
/** Max power for summation. */
private static final int MAX_POWER = 22;
/** An array that contains the objects needed to build the Hansen coefficients. <br/>
* The index is s */
private final FieldHansenThirdBodyLinear<T>[] hansenObjects;
/** Simple constructor.
* @param field field used by default
*/
@SuppressWarnings("unchecked")
FieldHansenObjects(final Field<T> field) {
this.hansenObjects = (FieldHansenThirdBodyLinear<T>[]) Array.newInstance(FieldHansenThirdBodyLinear.class, MAX_POWER + 1);
for (int s = 0; s <= MAX_POWER; s++) {
this.hansenObjects[s] = new FieldHansenThirdBodyLinear<>(MAX_POWER, s, field);
}
}
/** Initialise the Hansen roots for third body problem.
* @param context container for attributes
* @param B = sqrt(1 - e²).
* @param element element of the array to compute the init values
*/
public void computeHansenObjectsInitValues(final FieldDSSTThirdBodyDynamicContext<T> context,
final T B, final int element) {
hansenObjects[element].computeInitValues(B, context.getBB(), context.getBBB());
}
/** Get the Hansen Objects.
* @return hansenObjects
*/
public FieldHansenThirdBodyLinear<T>[] getHansenObjects() {
return hansenObjects;
}
}
}