FieldKeplerianOrbit.java
/* Copyright 2002-2017 CS Systèmes d'Information
* Licensed to CS Systèmes d'Information (CS) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* CS licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
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package org.orekit.orbits;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.stream.Collectors;
import java.util.stream.Stream;
import org.hipparchus.Field;
import org.hipparchus.RealFieldElement;
import org.hipparchus.analysis.differentiation.FDSFactory;
import org.hipparchus.analysis.differentiation.FieldDerivativeStructure;
import org.hipparchus.analysis.interpolation.FieldHermiteInterpolator;
import org.hipparchus.exception.MathIllegalArgumentException;
import org.hipparchus.geometry.euclidean.threed.FieldVector3D;
import org.hipparchus.util.FastMath;
import org.hipparchus.util.MathArrays;
import org.hipparchus.util.Precision;
import org.orekit.errors.OrekitIllegalArgumentException;
import org.orekit.errors.OrekitInternalError;
import org.orekit.errors.OrekitMessages;
import org.orekit.frames.Frame;
import org.orekit.time.FieldAbsoluteDate;
import org.orekit.utils.FieldPVCoordinates;
import org.orekit.utils.TimeStampedFieldPVCoordinates;
/**
* This class handles traditional Keplerian orbital parameters.
* <p>
* The parameters used internally are the classical Keplerian elements:
* <pre>
* a
* e
* i
* ω
* Ω
* v
* </pre>
* where ω stands for the Perigee Argument, Ω stands for the
* Right Ascension of the Ascending Node and v stands for the true anomaly.
* </p>
* <p>
* This class supports hyperbolic orbits, using the convention that semi major
* axis is negative for such orbits (and of course eccentricity is greater than 1).
* </p>
* <p>
* When orbit is either equatorial or circular, some Keplerian elements
* (more precisely ω and Ω) become ambiguous so this class should not
* be used for such orbits. For this reason, {@link EquinoctialOrbit equinoctial
* orbits} is the recommended way to represent orbits.
* </p>
* <p>
* The instance <code>KeplerianOrbit</code> is guaranteed to be immutable.
* </p>
* @see Orbit
* @see CircularOrbit
* @see CartesianOrbit
* @see EquinoctialOrbit
* @author Luc Maisonobe
* @author Guylaine Prat
* @author Fabien Maussion
* @author Véronique Pommier-Maurussane
* @author Andrea Antolino
* @since 9.0
*/
public class FieldKeplerianOrbit<T extends RealFieldElement<T>> extends FieldOrbit<T> {
/** Factory for first time derivatives. */
private static final Map<Field<? extends RealFieldElement<?>>, FDSFactory<? extends RealFieldElement<?>>> FACTORIES =
new HashMap<>();
/** First coefficient to compute Kepler equation solver starter. */
private static final double A;
/** Second coefficient to compute Kepler equation solver starter. */
private static final double B;
static {
final double k1 = 3 * FastMath.PI + 2;
final double k2 = FastMath.PI - 1;
final double k3 = 6 * FastMath.PI - 1;
A = 3 * k2 * k2 / k1;
B = k3 * k3 / (6 * k1);
}
/** Semi-major axis (m). */
private final T a;
/** Eccentricity. */
private final T e;
/** Inclination (rad). */
private final T i;
/** Perigee Argument (rad). */
private final T pa;
/** Right Ascension of Ascending Node (rad). */
private final T raan;
/** True anomaly (rad). */
private final T v;
/** Semi-major axis derivative (m/s). */
private final T aDot;
/** Eccentricity derivative. */
private final T eDot;
/** Inclination derivative (rad/s). */
private final T iDot;
/** Perigee Argument derivative (rad/s). */
private final T paDot;
/** Right Ascension of Ascending Node derivative (rad/s). */
private final T raanDot;
/** True anomaly derivative (rad/s). */
private final T vDot;
/** Partial Cartesian coordinates (position and velocity are valid, acceleration may be missing). */
private FieldPVCoordinates<T> partialPV;
/** Identity element. */
private final T one;
/** Zero element. */
private final T zero;
/** Third Canonical Vector. */
private final FieldVector3D<T> PLUS_K;
/** Creates a new instance.
* @param a semi-major axis (m), negative for hyperbolic orbits
* @param e eccentricity
* @param i inclination (rad)
* @param pa perigee argument (ω, rad)
* @param raan right ascension of ascending node (Ω, rad)
* @param anomaly mean, eccentric or true anomaly (rad)
* @param type type of anomaly
* @param frame the frame in which the parameters are defined
* (<em>must</em> be a {@link Frame#isPseudoInertial pseudo-inertial frame})
* @param date date of the orbital parameters
* @param mu central attraction coefficient (m³/s²)
* @exception IllegalArgumentException if frame is not a {@link
* Frame#isPseudoInertial pseudo-inertial frame} or a and e don't match for hyperbolic orbits,
* or v is out of range for hyperbolic orbits
*/
public FieldKeplerianOrbit(final T a, final T e, final T i,
final T pa, final T raan,
final T anomaly, final PositionAngle type,
final Frame frame, final FieldAbsoluteDate<T> date, final double mu)
throws IllegalArgumentException {
this(a, e, i, pa, raan, anomaly,
null, null, null, null, null, null,
type, frame, date, mu);
}
/** Creates a new instance.
* @param a semi-major axis (m), negative for hyperbolic orbits
* @param e eccentricity
* @param i inclination (rad)
* @param pa perigee argument (ω, rad)
* @param raan right ascension of ascending node (Ω, rad)
* @param anomaly mean, eccentric or true anomaly (rad)
* @param aDot semi-major axis derivative, null if unknown (m/s)
* @param eDot eccentricity derivative, null if unknown
* @param iDot inclination derivative, null if unknown (rad/s)
* @param paDot perigee argument derivative, null if unknown (rad/s)
* @param raanDot right ascension of ascending node derivative, null if unknown (rad/s)
* @param anomalyDot mean, eccentric or true anomaly derivative, null if unknown (rad/s)
* @param type type of anomaly
* @param frame the frame in which the parameters are defined
* (<em>must</em> be a {@link Frame#isPseudoInertial pseudo-inertial frame})
* @param date date of the orbital parameters
* @param mu central attraction coefficient (m³/s²)
* @exception IllegalArgumentException if frame is not a {@link
* Frame#isPseudoInertial pseudo-inertial frame} or a and e don't match for hyperbolic orbits,
* or v is out of range for hyperbolic orbits
*/
public FieldKeplerianOrbit(final T a, final T e, final T i,
final T pa, final T raan, final T anomaly,
final T aDot, final T eDot, final T iDot,
final T paDot, final T raanDot, final T anomalyDot,
final PositionAngle type,
final Frame frame, final FieldAbsoluteDate<T> date, final double mu)
throws IllegalArgumentException {
super(frame, date, mu);
if (a.multiply(e.negate().add(1)).getReal() < 0) {
throw new OrekitIllegalArgumentException(OrekitMessages.ORBIT_A_E_MISMATCH_WITH_CONIC_TYPE, a.getReal(), e.getReal());
}
if (!FACTORIES.containsKey(a.getField())) {
FACTORIES.put(a.getField(), new FDSFactory<>(a.getField(), 1, 1));
}
this.a = a;
this.aDot = aDot;
this.e = e;
this.eDot = eDot;
this.i = i;
this.iDot = iDot;
this.pa = pa;
this.paDot = paDot;
this.raan = raan;
this.raanDot = raanDot;
/** Identity element. */
this.one = a.getField().getOne();
/** Zero element. */
this.zero = a.getField().getZero();
/**Third canonical vector. */
this.PLUS_K = FieldVector3D.getPlusK(a.getField());
if (hasDerivatives()) {
@SuppressWarnings("unchecked")
final FDSFactory<T> factory = (FDSFactory<T>) FACTORIES.get(a.getField());
final FieldDerivativeStructure<T> eDS = factory.build(e, eDot);
final FieldDerivativeStructure<T> anomalyDS = factory.build(anomaly, anomalyDot);
final FieldDerivativeStructure<T> vDS;
switch (type) {
case MEAN :
vDS = (a.getReal() < 0) ?
hyperbolicEccentricToTrue(meanToHyperbolicEccentric(anomalyDS, eDS), eDS) :
ellipticEccentricToTrue(meanToEllipticEccentric(anomalyDS, eDS), eDS);
break;
case ECCENTRIC :
vDS = (a.getReal() < 0) ?
hyperbolicEccentricToTrue(anomalyDS, eDS) :
ellipticEccentricToTrue(anomalyDS, eDS);
break;
case TRUE :
vDS = anomalyDS;
break;
default : // this should never happen
throw new OrekitInternalError(null);
}
this.v = vDS.getValue();
this.vDot = vDS.getPartialDerivative(1);
} else {
switch (type) {
case MEAN :
this.v = (a.getReal() < 0) ?
hyperbolicEccentricToTrue(meanToHyperbolicEccentric(anomaly, e), e) :
ellipticEccentricToTrue(meanToEllipticEccentric(anomaly, e), e);
break;
case ECCENTRIC :
this.v = (a.getReal() < 0) ?
hyperbolicEccentricToTrue(anomaly, e) :
ellipticEccentricToTrue(anomaly, e);
break;
case TRUE :
this.v = anomaly;
break;
default : // this should never happen
throw new OrekitInternalError(null);
}
this.vDot = null;
}
// check true anomaly range
if (e.multiply(v.cos()).add(1).getReal() <= 0) {
final double vMax = e.reciprocal().negate().acos().getReal();
throw new OrekitIllegalArgumentException(OrekitMessages.ORBIT_ANOMALY_OUT_OF_HYPERBOLIC_RANGE,
v.getReal(), e.getReal(), -vMax, vMax);
}
this.partialPV = null;
}
/** Constructor from Cartesian parameters.
*
* <p> The acceleration provided in {@code FieldPVCoordinates} is accessible using
* {@link #getPVCoordinates()} and {@link #getPVCoordinates(Frame)}. All other methods
* use {@code mu} and the position to compute the acceleration, including
* {@link #shiftedBy(RealFieldElement)} and {@link #getPVCoordinates(FieldAbsoluteDate, Frame)}.
*
* @param pvCoordinates the PVCoordinates of the satellite
* @param frame the frame in which are defined the {@link FieldPVCoordinates}
* (<em>must</em> be a {@link Frame#isPseudoInertial pseudo-inertial frame})
* @param mu central attraction coefficient (m³/s²)
* @exception IllegalArgumentException if frame is not a {@link
* Frame#isPseudoInertial pseudo-inertial frame}
*/
public FieldKeplerianOrbit(final TimeStampedFieldPVCoordinates<T> pvCoordinates,
final Frame frame, final double mu)
throws IllegalArgumentException {
this(pvCoordinates, frame, mu, hasNonKeplerianAcceleration(pvCoordinates, mu));
}
/** Constructor from Cartesian parameters.
*
* <p> The acceleration provided in {@code FieldPVCoordinates} is accessible using
* {@link #getPVCoordinates()} and {@link #getPVCoordinates(Frame)}. All other methods
* use {@code mu} and the position to compute the acceleration, including
* {@link #shiftedBy(RealFieldElement)} and {@link #getPVCoordinates(FieldAbsoluteDate, Frame)}.
*
* @param pvCoordinates the PVCoordinates of the satellite
* @param frame the frame in which are defined the {@link FieldPVCoordinates}
* (<em>must</em> be a {@link Frame#isPseudoInertial pseudo-inertial frame})
* @param mu central attraction coefficient (m³/s²)
* @param reliableAcceleration if true, the acceleration is considered to be reliable
* @exception IllegalArgumentException if frame is not a {@link
* Frame#isPseudoInertial pseudo-inertial frame}
*/
private FieldKeplerianOrbit(final TimeStampedFieldPVCoordinates<T> pvCoordinates,
final Frame frame, final double mu,
final boolean reliableAcceleration)
throws IllegalArgumentException {
super(pvCoordinates, frame, mu);
// identity element
this.one = pvCoordinates.getPosition().getX().getField().getOne();
// zero element
this.zero = one.getField().getZero();
// third canonical vector
this.PLUS_K = FieldVector3D.getPlusK(one.getField());
// compute inclination
final FieldVector3D<T> momentum = pvCoordinates.getMomentum();
final T m2 = momentum.getNormSq();
i = FieldVector3D.angle(momentum, PLUS_K);
// compute right ascension of ascending node
raan = FieldVector3D.crossProduct(PLUS_K, momentum).getAlpha();
// preliminary computations for parameters depending on orbit shape (elliptic or hyperbolic)
final FieldVector3D<T> pvP = pvCoordinates.getPosition();
final FieldVector3D<T> pvV = pvCoordinates.getVelocity();
final FieldVector3D<T> pvA = pvCoordinates.getAcceleration();
final T r2 = pvP.getNormSq();
final T r = r2.sqrt();
final T V2 = pvV.getNormSq();
final T rV2OnMu = r.multiply(V2).divide(mu);
// compute semi-major axis (will be negative for hyperbolic orbits)
a = r.divide(rV2OnMu.negate().add(2.0));
final T muA = a.multiply(mu);
// compute true anomaly
if (a.getReal() > 0) {
// elliptic or circular orbit
final T eSE = FieldVector3D.dotProduct(pvP, pvV).divide(muA.sqrt());
final T eCE = rV2OnMu.subtract(1);
e = (eSE.multiply(eSE).add(eCE.multiply(eCE))).sqrt();
v = ellipticEccentricToTrue(eSE.atan2(eCE), e); //(atan2(eSE, eCE));
} else {
// hyperbolic orbit
final T eSH = FieldVector3D.dotProduct(pvP, pvV).divide(muA.negate().sqrt());
final T eCH = rV2OnMu.subtract(1);
e = (m2.negate().divide(muA).add(1)).sqrt();
v = hyperbolicEccentricToTrue((eCH.add(eSH)).divide(eCH.subtract(eSH)).log().divide(2), e);
}
// compute perigee argument
final FieldVector3D<T> node = new FieldVector3D<>(raan, zero);
final T px = FieldVector3D.dotProduct(pvP, node);
final T py = FieldVector3D.dotProduct(pvP, FieldVector3D.crossProduct(momentum, node)).divide(m2.sqrt());
pa = py.atan2(px).subtract(v);
partialPV = pvCoordinates;
if (!FACTORIES.containsKey(a.getField())) {
FACTORIES.put(a.getField(), new FDSFactory<>(a.getField(), 1, 1));
}
if (reliableAcceleration) {
// we have a relevant acceleration, we can compute derivatives
final T[][] jacobian = MathArrays.buildArray(a.getField(), 6, 6);
getJacobianWrtCartesian(PositionAngle.MEAN, jacobian);
final FieldVector3D<T> keplerianAcceleration = new FieldVector3D<>(r.multiply(r2).reciprocal().multiply(-mu), pvP);
final FieldVector3D<T> nonKeplerianAcceleration = pvA.subtract(keplerianAcceleration);
final T aX = nonKeplerianAcceleration.getX();
final T aY = nonKeplerianAcceleration.getY();
final T aZ = nonKeplerianAcceleration.getZ();
aDot = jacobian[0][3].multiply(aX).add(jacobian[0][4].multiply(aY)).add(jacobian[0][5].multiply(aZ));
eDot = jacobian[1][3].multiply(aX).add(jacobian[1][4].multiply(aY)).add(jacobian[1][5].multiply(aZ));
iDot = jacobian[2][3].multiply(aX).add(jacobian[2][4].multiply(aY)).add(jacobian[2][5].multiply(aZ));
paDot = jacobian[3][3].multiply(aX).add(jacobian[3][4].multiply(aY)).add(jacobian[3][5].multiply(aZ));
raanDot = jacobian[4][3].multiply(aX).add(jacobian[4][4].multiply(aY)).add(jacobian[4][5].multiply(aZ));
// in order to compute true anomaly derivative, we must compute
// mean anomaly derivative including Keplerian motion and convert to true anomaly
final T MDot = getKeplerianMeanMotion().
add(jacobian[5][3].multiply(aX)).add(jacobian[5][4].multiply(aY)).add(jacobian[5][5].multiply(aZ));
@SuppressWarnings("unchecked")
final FDSFactory<T> factory = (FDSFactory<T>) FACTORIES.get(a.getField());
final FieldDerivativeStructure<T> eDS = factory.build(e, eDot);
final FieldDerivativeStructure<T> MDS = factory.build(getMeanAnomaly(), MDot);
final FieldDerivativeStructure<T> vDS = (a.getReal() < 0) ?
FieldKeplerianOrbit.hyperbolicEccentricToTrue(FieldKeplerianOrbit.meanToHyperbolicEccentric(MDS, eDS), eDS) :
FieldKeplerianOrbit.ellipticEccentricToTrue(FieldKeplerianOrbit.meanToEllipticEccentric(MDS, eDS), eDS);
vDot = vDS.getPartialDerivative(1);
} else {
// acceleration is either almost zero or NaN,
// we assume acceleration was not known
// we don't set up derivatives
aDot = null;
eDot = null;
iDot = null;
paDot = null;
raanDot = null;
vDot = null;
}
}
/** Constructor from Cartesian parameters.
*
* <p> The acceleration provided in {@code FieldPVCoordinates} is accessible using
* {@link #getPVCoordinates()} and {@link #getPVCoordinates(Frame)}. All other methods
* use {@code mu} and the position to compute the acceleration, including
* {@link #shiftedBy(RealFieldElement)} and {@link #getPVCoordinates(FieldAbsoluteDate, Frame)}.
*
* @param FieldPVCoordinates the PVCoordinates of the satellite
* @param frame the frame in which are defined the {@link FieldPVCoordinates}
* (<em>must</em> be a {@link Frame#isPseudoInertial pseudo-inertial frame})
* @param date date of the orbital parameters
* @param mu central attraction coefficient (m³/s²)
* @exception IllegalArgumentException if frame is not a {@link
* Frame#isPseudoInertial pseudo-inertial frame}
*/
public FieldKeplerianOrbit(final FieldPVCoordinates<T> FieldPVCoordinates,
final Frame frame, final FieldAbsoluteDate<T> date, final double mu)
throws IllegalArgumentException {
this(new TimeStampedFieldPVCoordinates<>(date, FieldPVCoordinates), frame, mu);
}
/** Constructor from any kind of orbital parameters.
* @param op orbital parameters to copy
*/
public FieldKeplerianOrbit(final FieldOrbit<T> op) {
this(op.getPVCoordinates(), op.getFrame(), op.getMu(), op.hasDerivatives());
}
/** {@inheritDoc} */
public OrbitType getType() {
return OrbitType.KEPLERIAN;
}
/** {@inheritDoc} */
public T getA() {
return a;
}
/** {@inheritDoc} */
public T getADot() {
return aDot;
}
/** {@inheritDoc} */
public T getE() {
return e;
}
/** {@inheritDoc} */
public T getEDot() {
return eDot;
}
/** {@inheritDoc} */
public T getI() {
return i;
}
/** {@inheritDoc} */
public T getIDot() {
return iDot;
}
/** Get the perigee argument.
* @return perigee argument (rad)
*/
public T getPerigeeArgument() {
return pa;
}
/** Get the perigee argument derivative.
* <p>
* If the orbit was created without derivatives, the value returned is null.
* </p>
* @return perigee argument derivative (rad/s)
*/
public T getPerigeeArgumentDot() {
return paDot;
}
/** Get the right ascension of the ascending node.
* @return right ascension of the ascending node (rad)
*/
public T getRightAscensionOfAscendingNode() {
return raan;
}
/** Get the right ascension of the ascending node derivative.
* <p>
* If the orbit was created without derivatives, the value returned is null.
* </p>
* @return right ascension of the ascending node derivative (rad/s)
*/
public T getRightAscensionOfAscendingNodeDot() {
return raanDot;
}
/** Get the true anomaly.
* @return true anomaly (rad)
*/
public T getTrueAnomaly() {
return v;
}
/** Get the true anomaly derivative.
* <p>
* If the orbit was created without derivatives, the value returned is null.
* </p>
* @return true anomaly derivative (rad/s)
*/
public T getTrueAnomalyDot() {
return vDot;
}
/** Get the eccentric anomaly.
* @return eccentric anomaly (rad)
*/
public T getEccentricAnomaly() {
return (a.getReal() < 0) ? trueToHyperbolicEccentric(v, e) : trueToEllipticEccentric(v, e);
}
/** Get the eccentric anomaly derivative.
* <p>
* If the orbit was created without derivatives, the value returned is null.
* </p>
* @return eccentric anomaly derivative (rad/s)
*/
public T getEccentricAnomalyDot() {
if (!hasDerivatives()) {
return null;
}
@SuppressWarnings("unchecked")
final FDSFactory<T> factory = (FDSFactory<T>) FACTORIES.get(a.getField());
final FieldDerivativeStructure<T> eDS = factory.build(e, eDot);
final FieldDerivativeStructure<T> vDS = factory.build(v, vDot);
final FieldDerivativeStructure<T> EDS = (a.getReal() < 0) ?
trueToHyperbolicEccentric(vDS, eDS) :
trueToEllipticEccentric(vDS, eDS);
return EDS.getPartialDerivative(1);
}
/** Get the mean anomaly.
* @return mean anomaly (rad)
*/
public T getMeanAnomaly() {
return (a.getReal() < 0) ?
hyperbolicEccentricToMean(trueToHyperbolicEccentric(v, e), e) :
ellipticEccentricToMean(trueToEllipticEccentric(v, e), e);
}
/** Get the mean anomaly derivative.
* <p>
* If the orbit was created without derivatives, the value returned is null.
* </p>
* @return mean anomaly derivative (rad/s)
*/
public T getMeanAnomalyDot() {
if (!hasDerivatives()) {
return null;
}
@SuppressWarnings("unchecked")
final FDSFactory<T> factory = (FDSFactory<T>) FACTORIES.get(a.getField());
final FieldDerivativeStructure<T> eDS = factory.build(e, eDot);
final FieldDerivativeStructure<T> vDS = factory.build(v, vDot);
final FieldDerivativeStructure<T> MDS = (a.getReal() < 0) ?
hyperbolicEccentricToMean(trueToHyperbolicEccentric(vDS, eDS), eDS) :
ellipticEccentricToMean(trueToEllipticEccentric(vDS, eDS), eDS);
return MDS.getPartialDerivative(1);
}
/** Get the anomaly.
* @param type type of the angle
* @return anomaly (rad)
*/
public T getAnomaly(final PositionAngle type) {
return (type == PositionAngle.MEAN) ? getMeanAnomaly() :
((type == PositionAngle.ECCENTRIC) ? getEccentricAnomaly() :
getTrueAnomaly());
}
/** Get the anomaly derivative.
* <p>
* If the orbit was created without derivatives, the value returned is null.
* </p>
* @param type type of the angle
* @return anomaly derivative (rad/s)
*/
public T getAnomalyDot(final PositionAngle type) {
return (type == PositionAngle.MEAN) ? getMeanAnomalyDot() :
((type == PositionAngle.ECCENTRIC) ? getEccentricAnomalyDot() :
getTrueAnomalyDot());
}
/** {@inheritDoc} */
@Override
public boolean hasDerivatives() {
return aDot != null;
}
/** Computes the true anomaly from the elliptic eccentric anomaly.
* @param E eccentric anomaly (rad)
* @param e eccentricity
* @param <T> type of the field elements
* @return v the true anomaly
*/
public static <T extends RealFieldElement<T>> T ellipticEccentricToTrue(final T E, final T e) {
final T beta = e.divide(e.multiply(e).negate().add(1).sqrt().add(1));
return E.add(beta.multiply(E.sin()).divide(beta.multiply(E.cos()).subtract(1).negate()).atan().multiply(2));
}
/** Computes the elliptic eccentric anomaly from the true anomaly.
* @param v true anomaly (rad)
* @param e eccentricity
* @param <T> type of the field elements
* @return E the elliptic eccentric anomaly
*/
public static <T extends RealFieldElement<T>> T trueToEllipticEccentric(final T v, final T e) {
final T beta = e.divide(e.multiply(e).negate().add(1).sqrt().add(1));
return v.subtract((beta.multiply(v.sin()).divide(beta.multiply(v.cos()).add(1))).atan().multiply(2));
}
/** Computes the true anomaly from the hyperbolic eccentric anomaly.
* @param H hyperbolic eccentric anomaly (rad)
* @param e eccentricity
* @param <T> type of the field elements
* @return v the true anomaly
*/
public static <T extends RealFieldElement<T>> T hyperbolicEccentricToTrue(final T H, final T e) {
final T s = e.add(1).divide(e.subtract(1)).sqrt();
final T tanH = H.multiply(0.5).tanh();
return s.multiply(tanH).atan().multiply(2);
}
/** Computes the hyperbolic eccentric anomaly from the true anomaly.
* @param v true anomaly (rad)
* @param e eccentricity
* @param <T> type of the field elements
* @return H the hyperbolic eccentric anomaly
*/
public static <T extends RealFieldElement<T>> T trueToHyperbolicEccentric(final T v, final T e) {
final T sinhH = e.multiply(e).subtract(1).sqrt().multiply(v.sin()).divide(e.multiply(v.cos()).add(1));
return sinhH.asinh();
}
/** Computes the mean anomaly from the hyperbolic eccentric anomaly.
* @param H hyperbolic eccentric anomaly (rad)
* @param e eccentricity
* @param <T> type of the field elements
* @return M the mean anomaly
*/
public static <T extends RealFieldElement<T>> T hyperbolicEccentricToMean(final T H, final T e) {
return e.multiply(H.sinh()).subtract(H);
}
/** Computes the elliptic eccentric anomaly from the mean anomaly.
* <p>
* The algorithm used here for solving Kepler equation has been published
* in: "Procedures for solving Kepler's Equation", A. W. Odell and
* R. H. Gooding, Celestial Mechanics 38 (1986) 307-334
* </p>
* @param M mean anomaly (rad)
* @param e eccentricity
* @param <T> type of the field elements
* @return v the true anomaly
*/
public static <T extends RealFieldElement<T>> T meanToEllipticEccentric(final T M, final T e) {
// reduce M to [-PI PI) interval
final T reducedM = normalizeAngle(M, M.getField().getZero());
// compute start value according to A. W. Odell and R. H. Gooding S12 starter
T E;
if (reducedM.abs().getReal() < 1.0 / 6.0) {
if (FastMath.abs(reducedM.getReal()) < Precision.SAFE_MIN) {
// this is an Orekit change to the S12 starter, mainly used when T is some kind of derivative structure.
// If reducedM is 0.0, the derivative of cbrt is infinite which induces NaN appearing later in
// the computation. As in this case E and M are almost equal, we initialize E with reducedM
E = reducedM;
} else {
// this is the standard S12 starter
E = reducedM.add(e.multiply( (reducedM.multiply(6).cbrt()).subtract(reducedM)));
}
} else {
if (reducedM.getReal() < 0) {
final T w = reducedM.add(FastMath.PI);
E = reducedM.add(e.multiply(w.multiply(A).divide(w.negate().add(B)).subtract(FastMath.PI).subtract(reducedM)));
} else {
final T w = reducedM.negate().add(FastMath.PI);
E = reducedM.add(e.multiply(w.multiply(A).divide(w.negate().add(B)).negate().subtract(reducedM).add(FastMath.PI)));
}
}
final T e1 = e.negate().add(1);
final boolean noCancellationRisk = (e1.getReal() + E.getReal() * E.getReal() / 6) >= 0.1;
// perform two iterations, each consisting of one Halley step and one Newton-Raphson step
for (int j = 0; j < 2; ++j) {
final T f;
T fd;
final T fdd = e.multiply(E.sin());
final T fddd = e.multiply(E.cos());
if (noCancellationRisk) {
f = (E.subtract(fdd)).subtract(reducedM);
fd = fddd.negate().add(1);
} else {
f = eMeSinE(E, e).subtract(reducedM);
final T s = E.multiply(0.5).sin();
fd = e1.add(e.multiply(s).multiply(s).multiply(2));
}
final T dee = f.multiply(fd).divide(f.multiply(fdd).multiply(0.5).subtract(fd.multiply(fd)));
// update eccentric anomaly, using expressions that limit underflow problems
final T w = fd.add(dee.multiply(fdd.add(dee.multiply(fddd.divide(3)))).multiply(0.5));
fd = fd.add(dee.multiply(fdd.add(dee.multiply(fddd).multiply(0.5))));
E = E.subtract(f.subtract(dee.multiply(fd.subtract(w))).divide(fd));
}
// expand the result back to original range
E = E.add(M).subtract(reducedM);
return E;
}
/** Accurate computation of E - e sin(E).
* <p>
* This method is used when E is close to 0 and e close to 1,
* i.e. near the perigee of almost parabolic orbits
* </p>
* @param E eccentric anomaly
* @param e eccentricity
* @param <T> Type of the field elements
* @return E - e sin(E)
*/
private static <T extends RealFieldElement<T>> T eMeSinE(final T E, final T e) {
T x = (e.negate().add(1)).multiply(E.sin());
final T mE2 = E.negate().multiply(E);
T term = E;
double d = 0;
// the inequality test below IS intentional and should NOT be replaced by a check with a small tolerance
for (T x0 = E.getField().getZero().add(Double.NaN); x.getReal() != x0.getReal();) {
d += 2;
term = term.multiply(mE2.divide(d * (d + 1)));
x0 = x;
x = x.subtract(term);
}
return x;
}
/** Computes the hyperbolic eccentric anomaly from the mean anomaly.
* <p>
* The algorithm used here for solving hyperbolic Kepler equation is
* Danby's iterative method (3rd order) with Vallado's initial guess.
* </p>
* @param M mean anomaly (rad)
* @param e eccentricity
* @param <T> Type of the field elements
* @return H the hyperbolic eccentric anomaly
*/
public static <T extends RealFieldElement<T>> T meanToHyperbolicEccentric(final T M, final T e) {
// Resolution of hyperbolic Kepler equation for Keplerian parameters
// Initial guess
T H;
if (e.getReal() < 1.6) {
if ((-FastMath.PI < M.getReal() && M.getReal() < 0.) || M.getReal() > FastMath.PI) {
H = M.subtract(e);
} else {
H = M.add(e);
}
} else {
if (e.getReal() < 3.6 && M.abs().getReal() > FastMath.PI) {
H = M.subtract(e.copySign(M));
} else {
H = M.divide(e.subtract(1));
}
}
// Iterative computation
int iter = 0;
do {
final T f3 = e.multiply(H.cosh());
final T f2 = e.multiply(H.sinh());
final T f1 = f3.subtract(1);
final T f0 = f2.subtract(H).subtract(M);
final T f12 = f1.multiply(2);
final T d = f0.divide(f12);
final T fdf = f1.subtract(d.multiply(f2));
final T ds = f0.divide(fdf);
final T shift = f0.divide(fdf.add(ds.multiply(ds.multiply(f3.divide(6)))));
H = H.subtract(shift);
if ((shift.abs().getReal()) <= 1.0e-12) {
return H;
}
} while (++iter < 50);
throw new MathIllegalArgumentException(OrekitMessages.UNABLE_TO_COMPUTE_HYPERBOLIC_ECCENTRIC_ANOMALY,
iter);
}
/** Computes the mean anomaly from the elliptic eccentric anomaly.
* @param E eccentric anomaly (rad)
* @param e eccentricity
* @param <T> type of the field elements
* @return M the mean anomaly
*/
public static <T extends RealFieldElement<T>> T ellipticEccentricToMean(final T E, final T e) {
return E.subtract(e.multiply(E.sin()));
}
/** Compute position from elliptic Keplerian parameters.
* @param a semi-major axis (m)
* @param e eccentricity
* @param i inclination (rad)
* @param pa Perigee Argument (rad)
* @param raan Right Ascension of Ascending Node (rad)
* @param v true anomaly (rad)
* @param mu central attraction coefficient (m³/s²)
* @param <T> type of the fiels elements
* @return position vector
*/
public static <T extends RealFieldElement<T>> FieldVector3D<T> ellipticKeplerianToPosition(final T a, final T e, final T i,
final T pa, final T raan, final T v,
final double mu) {
// preliminary variables
final T cosRaan = raan.cos();
final T sinRaan = raan.sin();
final T cosPa = pa.cos();
final T sinPa = pa.sin();
final T cosI = i.cos();
final T sinI = i.sin();
final T crcp = cosRaan.multiply(cosPa);
final T crsp = cosRaan.multiply(sinPa);
final T srcp = sinRaan.multiply(cosPa);
final T srsp = sinRaan.multiply(sinPa);
// reference axes defining the orbital plane
final FieldVector3D<T> p = new FieldVector3D<>(crcp.subtract(cosI.multiply(srsp)), srcp.add(cosI.multiply(crsp)), sinI.multiply(sinPa));
final FieldVector3D<T> q = new FieldVector3D<>(crsp.add(cosI.multiply(srcp)).negate(), cosI.multiply(crcp).subtract(srsp), sinI.multiply(cosPa));
// elliptic eccentric anomaly
final T uME2 = e.negate().add(1).multiply(e.add(1));
final T s1Me2 = uME2.sqrt();
final T E = (a.getReal() < 0) ? trueToHyperbolicEccentric(v, e) : trueToEllipticEccentric(v, e);
final T cosE = E.cos();
final T sinE = E.sin();
// coordinates of position in the orbital plane
final T x = a.multiply(cosE.subtract(e));
final T y = a.multiply(sinE).multiply(s1Me2);
return new FieldVector3D<>(x, p, y, q);
}
/** Compute position from hyperbolic Keplerian parameters.
* @param a semi-major axis (m)
* @param e eccentricity
* @param i inclination (rad)
* @param pa Perigee Argument (rad)
* @param raan Right Ascension of Ascending Node (rad)
* @param v true anomaly (rad)
* @param mu central attraction coefficient (m³/s²)
* @param <T> type of the fiels elements
* @return position vector
*/
public static <T extends RealFieldElement<T>> FieldVector3D<T> hyperbolicKeplerianToPosition(final T a, final T e, final T i,
final T pa, final T raan, final T v,
final double mu) {
// preliminary variables
final T cosRaan = raan.cos();
final T sinRaan = raan.sin();
final T cosPa = pa.cos();
final T sinPa = pa.sin();
final T cosI = i.cos();
final T sinI = i.sin();
final T crcp = cosRaan.multiply(cosPa);
final T crsp = cosRaan.multiply(sinPa);
final T srcp = sinRaan.multiply(cosPa);
final T srsp = sinRaan.multiply(sinPa);
// reference axes defining the orbital plane
final FieldVector3D<T> p = new FieldVector3D<>(crcp.subtract(cosI.multiply(srsp)), srcp.add(cosI.multiply(crsp)), sinI.multiply(sinPa));
final FieldVector3D<T> q = new FieldVector3D<>(crsp.add(cosI.multiply(srcp)).negate(), cosI.multiply(crcp).subtract(srsp), sinI.multiply(cosPa));
// coordinates of position in the orbital plane
final T sinV = v.sin();
final T cosV = v.cos();
final T f = a.multiply(e.multiply(e).negate().add(1));
final T posFactor = f.divide(e.multiply(cosV).add(1));
final T x = posFactor.multiply(cosV);
final T y = posFactor.multiply(sinV);
return new FieldVector3D<>(x, p, y, q);
}
/** {@inheritDoc} */
public T getEquinoctialEx() {
return e.multiply(pa.add(raan).cos());
}
/** {@inheritDoc} */
public T getEquinoctialExDot() {
if (!hasDerivatives()) {
return null;
}
@SuppressWarnings("unchecked")
final FDSFactory<T> factory = (FDSFactory<T>) FACTORIES.get(a.getField());
final FieldDerivativeStructure<T> eDS = factory.build(e, eDot);
final FieldDerivativeStructure<T> paDS = factory.build(pa, paDot);
final FieldDerivativeStructure<T> raanDS = factory.build(raan, raanDot);
return eDS.multiply(paDS.add(raanDS).cos()).getPartialDerivative(1);
}
/** {@inheritDoc} */
public T getEquinoctialEy() {
return e.multiply((pa.add(raan)).sin());
}
/** {@inheritDoc} */
public T getEquinoctialEyDot() {
if (!hasDerivatives()) {
return null;
}
@SuppressWarnings("unchecked")
final FDSFactory<T> factory = (FDSFactory<T>) FACTORIES.get(a.getField());
final FieldDerivativeStructure<T> eDS = factory.build(e, eDot);
final FieldDerivativeStructure<T> paDS = factory.build(pa, paDot);
final FieldDerivativeStructure<T> raanDS = factory.build(raan, raanDot);
return eDS.multiply(paDS.add(raanDS).sin()).getPartialDerivative(1);
}
/** {@inheritDoc} */
public T getHx() {
// Check for equatorial retrograde orbit
if (FastMath.abs(i.getReal() - FastMath.PI) < 1.0e-10) {
return this.zero.add(Double.NaN);
}
return raan.cos().multiply(i.divide(2).tan());
}
/** {@inheritDoc} */
public T getHxDot() {
if (!hasDerivatives()) {
return null;
}
// Check for equatorial retrograde orbit
if (FastMath.abs(i.getReal() - FastMath.PI) < 1.0e-10) {
return this.zero.add(Double.NaN);
}
@SuppressWarnings("unchecked")
final FDSFactory<T> factory = (FDSFactory<T>) FACTORIES.get(a.getField());
final FieldDerivativeStructure<T> iDS = factory.build(i, iDot);
final FieldDerivativeStructure<T> raanDS = factory.build(raan, raanDot);
return raanDS.cos().multiply(iDS.multiply(0.5).tan()).getPartialDerivative(1);
}
/** {@inheritDoc} */
public T getHy() {
// Check for equatorial retrograde orbit
if (FastMath.abs(i.getReal() - FastMath.PI) < 1.0e-10) {
return this.zero.add(Double.NaN);
}
return raan.sin().multiply(i.divide(2).tan());
}
/** {@inheritDoc} */
public T getHyDot() {
if (!hasDerivatives()) {
return null;
}
// Check for equatorial retrograde orbit
if (FastMath.abs(i.getReal() - FastMath.PI) < 1.0e-10) {
return this.zero.add(Double.NaN);
}
@SuppressWarnings("unchecked")
final FDSFactory<T> factory = (FDSFactory<T>) FACTORIES.get(a.getField());
final FieldDerivativeStructure<T> iDS = factory.build(i, iDot);
final FieldDerivativeStructure<T> raanDS = factory.build(raan, raanDot);
return raanDS.sin().multiply(iDS.multiply(0.5).tan()).getPartialDerivative(1);
}
/** {@inheritDoc} */
public T getLv() {
return pa.add(raan).add(v);
}
/** {@inheritDoc} */
public T getLvDot() {
return hasDerivatives() ?
paDot.add(raanDot).add(vDot) :
null;
}
/** {@inheritDoc} */
public T getLE() {
return pa.add(raan).add(getEccentricAnomaly());
}
/** {@inheritDoc} */
public T getLEDot() {
return hasDerivatives() ?
paDot.add(raanDot).add(getEccentricAnomalyDot()) :
null;
}
/** {@inheritDoc} */
public T getLM() {
return pa.add(raan).add(getMeanAnomaly());
}
/** {@inheritDoc} */
public T getLMDot() {
return hasDerivatives() ?
paDot.add(raanDot).add(getMeanAnomalyDot()) :
null;
}
/** Compute position and velocity but not acceleration.
*/
private void computePVWithoutA() {
if (partialPV != null) {
// already computed
return;
}
// preliminary variables
final T cosRaan = raan.cos();
final T sinRaan = raan.sin();
final T cosPa = pa.cos();
final T sinPa = pa.sin();
final T cosI = i.cos();
final T sinI = i.sin();
final T crcp = cosRaan.multiply(cosPa);
final T crsp = cosRaan.multiply(sinPa);
final T srcp = sinRaan.multiply(cosPa);
final T srsp = sinRaan.multiply(sinPa);
// reference axes defining the orbital plane
final FieldVector3D<T> p = new FieldVector3D<>(crcp.subtract(cosI.multiply(srsp)), srcp.add(cosI.multiply(crsp)), sinI.multiply(sinPa));
final FieldVector3D<T> q = new FieldVector3D<>(crsp.add(cosI.multiply(srcp)).negate(), cosI.multiply(crcp).subtract(srsp), sinI.multiply(cosPa));
if (a.getReal() > 0) {
// elliptical case
// elliptic eccentric anomaly
final T uME2 = e.negate().add(1).multiply(e.add(1));
final T s1Me2 = uME2.sqrt();
final T E = getEccentricAnomaly();
final T cosE = E.cos();
final T sinE = E.sin();
// coordinates of position and velocity in the orbital plane
final T x = a.multiply(cosE.subtract(e));
final T y = a.multiply(sinE).multiply(s1Me2);
final T factor = (a.reciprocal().multiply(getMu())).sqrt().divide(e.negate().multiply(cosE).add(1));
final T xDot = sinE.negate().multiply(factor);
final T yDot = cosE.multiply(s1Me2).multiply(factor);
final FieldVector3D<T> position = new FieldVector3D<>(x, p, y, q);
final FieldVector3D<T> velocity = new FieldVector3D<>(xDot, p, yDot, q);
partialPV = new FieldPVCoordinates<>(position, velocity);
} else {
// hyperbolic case
// compute position and velocity factors
final T sinV = v.sin();
final T cosV = v.cos();
final T f = a.multiply(e.multiply(e).negate().add(1));
final T posFactor = f.divide(e.multiply(cosV).add(1));
final T velFactor = f.reciprocal().multiply(getMu()).sqrt();
final FieldVector3D<T> position = new FieldVector3D<>(posFactor.multiply(cosV), p, posFactor.multiply(sinV), q);
final FieldVector3D<T> velocity = new FieldVector3D<>(velFactor.multiply(sinV).negate(), p, velFactor.multiply(e.add(cosV)), q);
partialPV = new FieldPVCoordinates<>(position, velocity);
}
}
/** Compute non-Keplerian part of the acceleration from first time derivatives.
* <p>
* This method should be called only when {@link #hasDerivatives()} returns true.
* </p>
* @return non-Keplerian part of the acceleration
*/
private FieldVector3D<T> nonKeplerianAcceleration() {
final T[][] dCdP = MathArrays.buildArray(a.getField(), 6, 6);
getJacobianWrtParameters(PositionAngle.MEAN, dCdP);
final T nonKeplerianMeanMotion = getMeanAnomalyDot().subtract(getKeplerianMeanMotion());
final T nonKeplerianAx = dCdP[3][0].multiply(aDot).
add(dCdP[3][1].multiply(eDot)).
add(dCdP[3][2].multiply(iDot)).
add(dCdP[3][3].multiply(paDot)).
add(dCdP[3][4].multiply(raanDot)).
add(dCdP[3][5].multiply(nonKeplerianMeanMotion));
final T nonKeplerianAy = dCdP[4][0].multiply(aDot).
add(dCdP[4][1].multiply(eDot)).
add(dCdP[4][2].multiply(iDot)).
add(dCdP[4][3].multiply(paDot)).
add(dCdP[4][4].multiply(raanDot)).
add(dCdP[4][5].multiply(nonKeplerianMeanMotion));
final T nonKeplerianAz = dCdP[5][0].multiply(aDot).
add(dCdP[5][1].multiply(eDot)).
add(dCdP[5][2].multiply(iDot)).
add(dCdP[5][3].multiply(paDot)).
add(dCdP[5][4].multiply(raanDot)).
add(dCdP[5][5].multiply(nonKeplerianMeanMotion));
return new FieldVector3D<>(nonKeplerianAx, nonKeplerianAy, nonKeplerianAz);
}
/** {@inheritDoc} */
protected TimeStampedFieldPVCoordinates<T> initPVCoordinates() {
// position and velocity
computePVWithoutA();
// acceleration
final T r2 = partialPV.getPosition().getNormSq();
final FieldVector3D<T> keplerianAcceleration = new FieldVector3D<>(r2.multiply(r2.sqrt()).reciprocal().multiply(-getMu()),
partialPV.getPosition());
final FieldVector3D<T> acceleration = hasDerivatives() ?
keplerianAcceleration.add(nonKeplerianAcceleration()) :
keplerianAcceleration;
return new TimeStampedFieldPVCoordinates<>(getDate(), partialPV.getPosition(), partialPV.getVelocity(), acceleration);
}
/** {@inheritDoc} */
public FieldKeplerianOrbit<T> shiftedBy(final double dt) {
return shiftedBy(getDate().getField().getZero().add(dt));
}
/** {@inheritDoc} */
public FieldKeplerianOrbit<T> shiftedBy(final T dt) {
// use Keplerian-only motion
final FieldKeplerianOrbit<T> keplerianShifted = new FieldKeplerianOrbit<>(a, e, i, pa, raan,
getKeplerianMeanMotion().multiply(dt).add(getMeanAnomaly()),
PositionAngle.MEAN, getFrame(), getDate().shiftedBy(dt), getMu());
if (hasDerivatives()) {
// extract non-Keplerian acceleration from first time derivatives
final FieldVector3D<T> nonKeplerianAcceleration = nonKeplerianAcceleration();
// add quadratic effect of non-Keplerian acceleration to Keplerian-only shift
keplerianShifted.computePVWithoutA();
final FieldVector3D<T> fixedP = new FieldVector3D<>(one, keplerianShifted.partialPV.getPosition(),
dt.multiply(dt).multiply(0.5), nonKeplerianAcceleration);
final T fixedR2 = fixedP.getNormSq();
final T fixedR = fixedR2.sqrt();
final FieldVector3D<T> fixedV = new FieldVector3D<>(one, keplerianShifted.partialPV.getVelocity(),
dt, nonKeplerianAcceleration);
final FieldVector3D<T> fixedA = new FieldVector3D<>(fixedR2.multiply(fixedR).reciprocal().multiply(-getMu()),
keplerianShifted.partialPV.getPosition(),
one, nonKeplerianAcceleration);
// build a new orbit, taking non-Keplerian acceleration into account
return new FieldKeplerianOrbit<>(new TimeStampedFieldPVCoordinates<>(keplerianShifted.getDate(),
fixedP, fixedV, fixedA),
keplerianShifted.getFrame(), keplerianShifted.getMu());
} else {
// Keplerian-only motion is all we can do
return keplerianShifted;
}
}
/** {@inheritDoc}
* <p>
* The interpolated instance is created by polynomial Hermite interpolation
* on Keplerian elements, without derivatives (which means the interpolation
* falls back to Lagrange interpolation only).
* </p>
* <p>
* As this implementation of interpolation is polynomial, it should be used only
* with small samples (about 10-20 points) in order to avoid <a
* href="http://en.wikipedia.org/wiki/Runge%27s_phenomenon">Runge's phenomenon</a>
* and numerical problems (including NaN appearing).
* </p>
* <p>
* If orbit interpolation on large samples is needed, using the {@link
* org.orekit.propagation.analytical.Ephemeris} class is a better way than using this
* low-level interpolation. The Ephemeris class automatically handles selection of
* a neighboring sub-sample with a predefined number of point from a large global sample
* in a thread-safe way.
* </p>
*/
public FieldKeplerianOrbit<T> interpolate(final FieldAbsoluteDate<T> date, final Stream<FieldOrbit<T>> sample) {
// first pass to check if derivatives are available throughout the sample
final List<FieldOrbit<T>> list = sample.collect(Collectors.toList());
boolean useDerivatives = true;
for (final FieldOrbit<T> orbit : list) {
useDerivatives = useDerivatives && orbit.hasDerivatives();
}
// set up an interpolator
final FieldHermiteInterpolator<T> interpolator = new FieldHermiteInterpolator<>();
// second pass to feed interpolator
FieldAbsoluteDate<T> previousDate = null;
T previousPA = zero.add(Double.NaN);
T previousRAAN = zero.add(Double.NaN);
T previousM = zero.add(Double.NaN);
for (final FieldOrbit<T> orbit : list) {
final FieldKeplerianOrbit<T> kep = (FieldKeplerianOrbit<T>) OrbitType.KEPLERIAN.convertType(orbit);
final T continuousPA;
final T continuousRAAN;
final T continuousM;
if (previousDate == null) {
continuousPA = kep.getPerigeeArgument();
continuousRAAN = kep.getRightAscensionOfAscendingNode();
continuousM = kep.getMeanAnomaly();
} else {
final T dt = kep.getDate().durationFrom(previousDate);
final T keplerM = previousM.add(kep.getKeplerianMeanMotion().multiply(dt));
continuousPA = normalizeAngle(kep.getPerigeeArgument(), previousPA);
continuousRAAN = normalizeAngle(kep.getRightAscensionOfAscendingNode(), previousRAAN);
continuousM = normalizeAngle(kep.getMeanAnomaly(), keplerM);
}
previousDate = kep.getDate();
previousPA = continuousPA;
previousRAAN = continuousRAAN;
previousM = continuousM;
final T[] toAdd = MathArrays.buildArray(getA().getField(), 6);
toAdd[0] = kep.getA();
toAdd[1] = kep.getE();
toAdd[2] = kep.getI();
toAdd[3] = continuousPA;
toAdd[4] = continuousRAAN;
toAdd[5] = continuousM;
if (useDerivatives) {
final T[] toAddDot = MathArrays.buildArray(one.getField(), 6);
toAddDot[0] = kep.getADot();
toAddDot[1] = kep.getEDot();
toAddDot[2] = kep.getIDot();
toAddDot[3] = kep.getPerigeeArgumentDot();
toAddDot[4] = kep.getRightAscensionOfAscendingNodeDot();
toAddDot[5] = kep.getMeanAnomalyDot();
interpolator.addSamplePoint(kep.getDate().durationFrom(date),
toAdd, toAddDot);
} else {
interpolator.addSamplePoint(this.zero.add(kep.getDate().durationFrom(date)),
toAdd);
}
}
// interpolate
final T[][] interpolated = interpolator.derivatives(zero, 1);
// build a new interpolated instance
return new FieldKeplerianOrbit<>(interpolated[0][0], interpolated[0][1], interpolated[0][2],
interpolated[0][3], interpolated[0][4], interpolated[0][5],
interpolated[1][0], interpolated[1][1], interpolated[1][2],
interpolated[1][3], interpolated[1][4], interpolated[1][5],
PositionAngle.MEAN, getFrame(), date, getMu());
}
/** {@inheritDoc} */
protected T[][] computeJacobianMeanWrtCartesian() {
if (a.getReal() > 0) {
return computeJacobianMeanWrtCartesianElliptical();
} else {
return computeJacobianMeanWrtCartesianHyperbolic();
}
}
/** Compute the Jacobian of the orbital parameters with respect to the Cartesian parameters.
* <p>
* Element {@code jacobian[i][j]} is the derivative of parameter i of the orbit with
* respect to Cartesian coordinate j (x for j=0, y for j=1, z for j=2, xDot for j=3,
* yDot for j=4, zDot for j=5).
* </p>
* @return 6x6 Jacobian matrix
*/
private T[][] computeJacobianMeanWrtCartesianElliptical() {
final T[][] jacobian = MathArrays.buildArray(getA().getField(), 6, 6);
// compute various intermediate parameters
computePVWithoutA();
final FieldVector3D<T> position = partialPV.getPosition();
final FieldVector3D<T> velocity = partialPV.getVelocity();
final FieldVector3D<T> momentum = partialPV.getMomentum();
final T v2 = velocity.getNormSq();
final T r2 = position.getNormSq();
final T r = r2.sqrt();
final T r3 = r.multiply(r2);
final T px = position.getX();
final T py = position.getY();
final T pz = position.getZ();
final T vx = velocity.getX();
final T vy = velocity.getY();
final T vz = velocity.getZ();
final T mx = momentum.getX();
final T my = momentum.getY();
final T mz = momentum.getZ();
final double mu = getMu();
final T sqrtMuA = a.multiply(mu).sqrt();
final T sqrtAoMu = a.divide(mu).sqrt();
final T a2 = a.multiply(a);
final T twoA = a.multiply(2);
final T rOnA = r.divide(a);
final T oMe2 = e.multiply(e).negate().add(1);
final T epsilon = oMe2.sqrt();
final T sqrtRec = epsilon.reciprocal();
final T cosI = i.cos();
final T sinI = i.sin();
final T cosPA = pa.cos();
final T sinPA = pa.sin();
final T pv = FieldVector3D.dotProduct(position, velocity);
final T cosE = a.subtract(r).divide(a.multiply(e));
final T sinE = pv.divide(e.multiply(sqrtMuA));
// da
final FieldVector3D<T> vectorAR = new FieldVector3D<>(a2.multiply(2).divide(r3), position);
final FieldVector3D<T> vectorARDot = velocity.scalarMultiply(a2.multiply(2 / mu));
fillHalfRow(this.one, vectorAR, jacobian[0], 0);
fillHalfRow(this.one, vectorARDot, jacobian[0], 3);
// de
final T factorER3 = pv.divide(twoA);
final FieldVector3D<T> vectorER = new FieldVector3D<>(cosE.multiply(v2).divide(r.multiply(mu)), position,
sinE.divide(sqrtMuA), velocity,
factorER3.negate().multiply(sinE).divide(sqrtMuA), vectorAR);
final FieldVector3D<T> vectorERDot = new FieldVector3D<>(sinE.divide(sqrtMuA), position,
cosE.multiply(2 / mu).multiply(r), velocity,
factorER3.negate().multiply(sinE).divide(sqrtMuA), vectorARDot);
fillHalfRow(this.one, vectorER, jacobian[1], 0);
fillHalfRow(this.one, vectorERDot, jacobian[1], 3);
// dE / dr (Eccentric anomaly)
final T coefE = cosE.divide(e.multiply(sqrtMuA));
final FieldVector3D<T> vectorEAnR =
new FieldVector3D<>(sinE.negate().multiply(v2).divide(e.multiply(r).multiply(mu)), position, coefE, velocity,
factorER3.negate().multiply(coefE), vectorAR);
// dE / drDot
final FieldVector3D<T> vectorEAnRDot =
new FieldVector3D<>(sinE.multiply(-2).multiply(r).divide(e.multiply(mu)), velocity, coefE, position,
factorER3.negate().multiply(coefE), vectorARDot);
// precomputing some more factors
final T s1 = sinE.negate().multiply(pz).divide(r).subtract(cosE.multiply(vz).multiply(sqrtAoMu));
final T s2 = cosE.negate().multiply(pz).divide(r3);
final T s3 = sinE.multiply(vz).divide(sqrtMuA.multiply(-2));
final T t1 = sqrtRec.multiply(cosE.multiply(pz).divide(r).subtract(sinE.multiply(vz).multiply(sqrtAoMu)));
final T t2 = sqrtRec.multiply(sinE.negate().multiply(pz).divide(r3));
final T t3 = sqrtRec.multiply(cosE.subtract(e)).multiply(vz).divide(sqrtMuA.multiply(2));
final T t4 = sqrtRec.multiply(e.multiply(sinI).multiply(cosPA).multiply(sqrtRec).subtract(vz.multiply(sqrtAoMu)));
final FieldVector3D<T> s = new FieldVector3D<>(cosE.divide(r), this.PLUS_K,
s1, vectorEAnR,
s2, position,
s3, vectorAR);
final FieldVector3D<T> sDot = new FieldVector3D<>(sinE.negate().multiply(sqrtAoMu), this.PLUS_K,
s1, vectorEAnRDot,
s3, vectorARDot);
final FieldVector3D<T> t =
new FieldVector3D<>(sqrtRec.multiply(sinE).divide(r), this.PLUS_K).add(new FieldVector3D<>(t1, vectorEAnR,
t2, position,
t3, vectorAR,
t4, vectorER));
final FieldVector3D<T> tDot = new FieldVector3D<>(sqrtRec.multiply(cosE.subtract(e)).multiply(sqrtAoMu), this.PLUS_K,
t1, vectorEAnRDot,
t3, vectorARDot,
t4, vectorERDot);
// di
final T factorI1 = sinI.negate().multiply(sqrtRec).divide(sqrtMuA);
final T i1 = factorI1;
final T i2 = factorI1.negate().multiply(mz).divide(twoA);
final T i3 = factorI1.multiply(mz).multiply(e).divide(oMe2);
final T i4 = cosI.multiply(sinPA);
final T i5 = cosI.multiply(cosPA);
fillHalfRow(i1, new FieldVector3D<>(vy, vx.negate(), this.zero), i2, vectorAR, i3, vectorER, i4, s, i5, t,
jacobian[2], 0);
fillHalfRow(i1, new FieldVector3D<>(py.negate(), px, this.zero), i2, vectorARDot, i3, vectorERDot, i4, sDot, i5, tDot,
jacobian[2], 3);
// dpa
fillHalfRow(cosPA.divide(sinI), s, sinPA.negate().divide(sinI), t, jacobian[3], 0);
fillHalfRow(cosPA.divide(sinI), sDot, sinPA.negate().divide(sinI), tDot, jacobian[3], 3);
// dRaan
final T factorRaanR = (a.multiply(mu).multiply(oMe2).multiply(sinI).multiply(sinI)).reciprocal();
fillHalfRow( factorRaanR.negate().multiply(my), new FieldVector3D<>(zero, vz, vy.negate()),
factorRaanR.multiply(mx), new FieldVector3D<>(vz.negate(), zero, vx),
jacobian[4], 0);
fillHalfRow(factorRaanR.negate().multiply(my), new FieldVector3D<>(zero, pz.negate(), py),
factorRaanR.multiply(mx), new FieldVector3D<>(pz, zero, px.negate()),
jacobian[4], 3);
// dM
fillHalfRow(rOnA, vectorEAnR, sinE.negate(), vectorER, jacobian[5], 0);
fillHalfRow(rOnA, vectorEAnRDot, sinE.negate(), vectorERDot, jacobian[5], 3);
return jacobian;
}
/** Compute the Jacobian of the orbital parameters with respect to the Cartesian parameters.
* <p>
* Element {@code jacobian[i][j]} is the derivative of parameter i of the orbit with
* respect to Cartesian coordinate j (x for j=0, y for j=1, z for j=2, xDot for j=3,
* yDot for j=4, zDot for j=5).
* </p>
* @return 6x6 Jacobian matrix
*/
private T[][] computeJacobianMeanWrtCartesianHyperbolic() {
final T[][] jacobian = MathArrays.buildArray(getA().getField(), 6, 6);
// compute various intermediate parameters
computePVWithoutA();
final FieldVector3D<T> position = partialPV.getPosition();
final FieldVector3D<T> velocity = partialPV.getVelocity();
final FieldVector3D<T> momentum = partialPV.getMomentum();
final T r2 = position.getNormSq();
final T r = r2.sqrt();
final T r3 = r.multiply(r2);
final T x = position.getX();
final T y = position.getY();
final T z = position.getZ();
final T vx = velocity.getX();
final T vy = velocity.getY();
final T vz = velocity.getZ();
final T mx = momentum.getX();
final T my = momentum.getY();
final T mz = momentum.getZ();
final double mu = getMu();
final T absA = a.negate();
final T sqrtMuA = absA.multiply(mu).sqrt();
final T a2 = a.multiply(a);
final T rOa = r.divide(absA);
final T cosI = i.cos();
final T sinI = i.sin();
final T pv = FieldVector3D.dotProduct(position, velocity);
// da
final FieldVector3D<T> vectorAR = new FieldVector3D<>(a2.multiply(-2).divide(r3), position);
final FieldVector3D<T> vectorARDot = velocity.scalarMultiply(a2.multiply(-2 / mu));
fillHalfRow(this.one.negate(), vectorAR, jacobian[0], 0);
fillHalfRow(this.one.negate(), vectorARDot, jacobian[0], 3);
// differentials of the momentum
final T m = momentum.getNorm();
final T oOm = m.reciprocal();
final FieldVector3D<T> dcXP = new FieldVector3D<>(this.zero, vz, vy.negate());
final FieldVector3D<T> dcYP = new FieldVector3D<>(vz.negate(), this.zero, vx);
final FieldVector3D<T> dcZP = new FieldVector3D<>( vy, vx.negate(), this.zero);
final FieldVector3D<T> dcXV = new FieldVector3D<>( this.zero, z.negate(), y);
final FieldVector3D<T> dcYV = new FieldVector3D<>( z, this.zero, x.negate());
final FieldVector3D<T> dcZV = new FieldVector3D<>( y.negate(), x, this.zero);
final FieldVector3D<T> dCP = new FieldVector3D<>(mx.multiply(oOm), dcXP, my.multiply(oOm), dcYP, mz.multiply(oOm), dcZP);
final FieldVector3D<T> dCV = new FieldVector3D<>(mx.multiply(oOm), dcXV, my.multiply(oOm), dcYV, mz.multiply(oOm), dcZV);
// dp
final T mOMu = m.divide(mu);
final FieldVector3D<T> dpP = new FieldVector3D<>(mOMu.multiply(2), dCP);
final FieldVector3D<T> dpV = new FieldVector3D<>(mOMu.multiply(2), dCV);
// de
final T p = m.multiply(mOMu);
final T moO2ae = absA.multiply(2).multiply(e).reciprocal();
final T m2OaMu = p.negate().divide(absA);
fillHalfRow(moO2ae, dpP, m2OaMu.multiply(moO2ae), vectorAR, jacobian[1], 0);
fillHalfRow(moO2ae, dpV, m2OaMu.multiply(moO2ae), vectorARDot, jacobian[1], 3);
// di
final T cI1 = m.multiply(sinI).reciprocal();
final T cI2 = cosI.multiply(cI1);
fillHalfRow(cI2, dCP, cI1.negate(), dcZP, jacobian[2], 0);
fillHalfRow(cI2, dCV, cI1.negate(), dcZV, jacobian[2], 3);
// dPA
final T cP1 = y.multiply(oOm);
final T cP2 = x.negate().multiply(oOm);
final T cP3 = mx.multiply(cP1).add(my.multiply(cP2)).negate();
final T cP4 = cP3.multiply(oOm);
final T cP5 = r2.multiply(sinI).multiply(sinI).negate().reciprocal();
final T cP6 = z.multiply(cP5);
final T cP7 = cP3.multiply(cP5);
final FieldVector3D<T> dacP = new FieldVector3D<>(cP1, dcXP, cP2, dcYP, cP4, dCP, oOm, new FieldVector3D<>(my.negate(), mx, this.zero));
final FieldVector3D<T> dacV = new FieldVector3D<>(cP1, dcXV, cP2, dcYV, cP4, dCV);
final FieldVector3D<T> dpoP = new FieldVector3D<>(cP6, dacP, cP7, this.PLUS_K);
final FieldVector3D<T> dpoV = new FieldVector3D<>(cP6, dacV);
final T re2 = r2.multiply(e).multiply(e);
final T recOre2 = p.subtract(r).divide(re2);
final T resOre2 = pv.multiply(mOMu).divide(re2);
final FieldVector3D<T> dreP = new FieldVector3D<>(mOMu, velocity, pv.divide(mu), dCP);
final FieldVector3D<T> dreV = new FieldVector3D<>(mOMu, position, pv.divide(mu), dCV);
final FieldVector3D<T> davP = new FieldVector3D<>(resOre2.negate(), dpP, recOre2, dreP, resOre2.divide(r), position);
final FieldVector3D<T> davV = new FieldVector3D<>(resOre2.negate(), dpV, recOre2, dreV);
fillHalfRow(this.one, dpoP, this.one.negate(), davP, jacobian[3], 0);
fillHalfRow(this.one, dpoV, this.one.negate(), davV, jacobian[3], 3);
// dRAAN
final T cO0 = cI1.multiply(cI1);
final T cO1 = mx.multiply(cO0);
final T cO2 = my.negate().multiply(cO0);
fillHalfRow(cO1, dcYP, cO2, dcXP, jacobian[4], 0);
fillHalfRow(cO1, dcYV, cO2, dcXV, jacobian[4], 3);
// dM
final T s2a = pv.divide(absA.multiply(2));
final T oObux = m.multiply(m).add(absA.multiply(mu)).sqrt().reciprocal();
final T scasbu = pv.multiply(oObux);
final FieldVector3D<T> dauP = new FieldVector3D<>(sqrtMuA.reciprocal(), velocity, s2a.negate().divide(sqrtMuA), vectorAR);
final FieldVector3D<T> dauV = new FieldVector3D<>(sqrtMuA.reciprocal(), position, s2a.negate().divide(sqrtMuA), vectorARDot);
final FieldVector3D<T> dbuP = new FieldVector3D<>(oObux.multiply(mu / 2), vectorAR, m.multiply(oObux), dCP);
final FieldVector3D<T> dbuV = new FieldVector3D<>(oObux.multiply(mu / 2), vectorARDot, m.multiply(oObux), dCV);
final FieldVector3D<T> dcuP = new FieldVector3D<>(oObux, velocity, scasbu.negate().multiply(oObux), dbuP);
final FieldVector3D<T> dcuV = new FieldVector3D<>(oObux, position, scasbu.negate().multiply(oObux), dbuV);
fillHalfRow(this.one, dauP, e.negate().divide(rOa.add(1)), dcuP, jacobian[5], 0);
fillHalfRow(this.one, dauV, e.negate().divide(rOa.add(1)), dcuV, jacobian[5], 3);
return jacobian;
}
/** {@inheritDoc} */
protected T[][] computeJacobianEccentricWrtCartesian() {
if (a.getReal() > 0) {
return computeJacobianEccentricWrtCartesianElliptical();
} else {
return computeJacobianEccentricWrtCartesianHyperbolic();
}
}
/** Compute the Jacobian of the orbital parameters with respect to the Cartesian parameters.
* <p>
* Element {@code jacobian[i][j]} is the derivative of parameter i of the orbit with
* respect to Cartesian coordinate j (x for j=0, y for j=1, z for j=2, xDot for j=3,
* yDot for j=4, zDot for j=5).
* </p>
* @return 6x6 Jacobian matrix
*/
private T[][] computeJacobianEccentricWrtCartesianElliptical() {
// start by computing the Jacobian with mean angle
final T[][] jacobian = computeJacobianMeanWrtCartesianElliptical();
// Differentiating the Kepler equation M = E - e sin E leads to:
// dM = (1 - e cos E) dE - sin E de
// which is inverted and rewritten as:
// dE = a/r dM + sin E a/r de
final T eccentricAnomaly = getEccentricAnomaly();
final T cosE = eccentricAnomaly.cos();
final T sinE = eccentricAnomaly.sin();
final T aOr = e.negate().multiply(cosE).add(1).reciprocal();
// update anomaly row
final T[] eRow = jacobian[1];
final T[] anomalyRow = jacobian[5];
for (int j = 0; j < anomalyRow.length; ++j) {
anomalyRow[j] = aOr.multiply(anomalyRow[j].add(sinE.multiply(eRow[j])));
}
return jacobian;
}
/** Compute the Jacobian of the orbital parameters with respect to the Cartesian parameters.
* <p>
* Element {@code jacobian[i][j]} is the derivative of parameter i of the orbit with
* respect to Cartesian coordinate j (x for j=0, y for j=1, z for j=2, xDot for j=3,
* yDot for j=4, zDot for j=5).
* </p>
* @return 6x6 Jacobian matrix
*/
private T[][] computeJacobianEccentricWrtCartesianHyperbolic() {
// start by computing the Jacobian with mean angle
final T[][] jacobian = computeJacobianMeanWrtCartesianHyperbolic();
// Differentiating the Kepler equation M = e sinh H - H leads to:
// dM = (e cosh H - 1) dH + sinh H de
// which is inverted and rewritten as:
// dH = 1 / (e cosh H - 1) dM - sinh H / (e cosh H - 1) de
final T H = getEccentricAnomaly();
final T coshH = H.cosh();
final T sinhH = H.sinh();
final T absaOr = e.multiply(coshH).subtract(1).reciprocal();
// update anomaly row
final T[] eRow = jacobian[1];
final T[] anomalyRow = jacobian[5];
for (int j = 0; j < anomalyRow.length; ++j) {
anomalyRow[j] = absaOr.multiply(anomalyRow[j].subtract(sinhH.multiply(eRow[j])));
}
return jacobian;
}
/** {@inheritDoc} */
protected T[][] computeJacobianTrueWrtCartesian() {
if (a.getReal() > 0) {
return computeJacobianTrueWrtCartesianElliptical();
} else {
return computeJacobianTrueWrtCartesianHyperbolic();
}
}
/** Compute the Jacobian of the orbital parameters with respect to the Cartesian parameters.
* <p>
* Element {@code jacobian[i][j]} is the derivative of parameter i of the orbit with
* respect to Cartesian coordinate j (x for j=0, y for j=1, z for j=2, xDot for j=3,
* yDot for j=4, zDot for j=5).
* </p>
* @return 6x6 Jacobian matrix
*/
private T[][] computeJacobianTrueWrtCartesianElliptical() {
// start by computing the Jacobian with eccentric angle
final T[][] jacobian = computeJacobianEccentricWrtCartesianElliptical();
// Differentiating the eccentric anomaly equation sin E = sqrt(1-e^2) sin v / (1 + e cos v)
// and using cos E = (e + cos v) / (1 + e cos v) to get rid of cos E leads to:
// dE = [sqrt (1 - e^2) / (1 + e cos v)] dv - [sin E / (1 - e^2)] de
// which is inverted and rewritten as:
// dv = sqrt (1 - e^2) a/r dE + [sin E / sqrt (1 - e^2)] a/r de
final T e2 = e.multiply(e);
final T oMe2 = e2.negate().add(1);
final T epsilon = oMe2.sqrt();
final T eccentricAnomaly = getEccentricAnomaly();
final T cosE = eccentricAnomaly.cos();
final T sinE = eccentricAnomaly.sin();
final T aOr = e.multiply(cosE).negate().add(1).reciprocal();
final T aFactor = epsilon.multiply(aOr);
final T eFactor = sinE.multiply(aOr).divide(epsilon);
// update anomaly row
final T[] eRow = jacobian[1];
final T[] anomalyRow = jacobian[5];
for (int j = 0; j < anomalyRow.length; ++j) {
anomalyRow[j] = aFactor.multiply(anomalyRow[j]).add(eFactor.multiply(eRow[j]));
}
return jacobian;
}
/** Compute the Jacobian of the orbital parameters with respect to the Cartesian parameters.
* <p>
* Element {@code jacobian[i][j]} is the derivative of parameter i of the orbit with
* respect to Cartesian coordinate j (x for j=0, y for j=1, z for j=2, xDot for j=3,
* yDot for j=4, zDot for j=5).
* </p>
* @return 6x6 Jacobian matrix
*/
private T[][] computeJacobianTrueWrtCartesianHyperbolic() {
// start by computing the Jacobian with eccentric angle
final T[][] jacobian = computeJacobianEccentricWrtCartesianHyperbolic();
// Differentiating the eccentric anomaly equation sinh H = sqrt(e^2-1) sin v / (1 + e cos v)
// and using cosh H = (e + cos v) / (1 + e cos v) to get rid of cosh H leads to:
// dH = [sqrt (e^2 - 1) / (1 + e cos v)] dv + [sinh H / (e^2 - 1)] de
// which is inverted and rewritten as:
// dv = sqrt (1 - e^2) a/r dH - [sinh H / sqrt (e^2 - 1)] a/r de
final T e2 = e.multiply(e);
final T e2Mo = e2.subtract(1);
final T epsilon = e2Mo.sqrt();
final T H = getEccentricAnomaly();
final T coshH = H.cosh();
final T sinhH = H.sinh();
final T aOr = e.multiply(coshH).subtract(1).reciprocal();
final T aFactor = epsilon.multiply(aOr);
final T eFactor = sinhH .multiply(aOr).divide(epsilon);
// update anomaly row
final T[] eRow = jacobian[1];
final T[] anomalyRow = jacobian[5];
for (int j = 0; j < anomalyRow.length; ++j) {
anomalyRow[j] = aFactor.multiply(anomalyRow[j]).subtract(eFactor.multiply(eRow[j]));
}
return jacobian;
}
/** {@inheritDoc} */
public void addKeplerContribution(final PositionAngle type, final double gm,
final T[] pDot) {
final T oMe2;
final T ksi;
final T absA = a.abs();
final T n = absA.reciprocal().multiply(gm).sqrt().divide(absA);
switch (type) {
case MEAN :
pDot[5] = pDot[5].add(n);
break;
case ECCENTRIC :
oMe2 = e.multiply(e).negate().add(1).abs();
ksi = e.multiply(v.cos()).add(1);
pDot[5] = pDot[5].add( n.multiply(ksi).divide(oMe2));
break;
case TRUE :
oMe2 = e.multiply(e).negate().add(1).abs();
ksi = e.multiply(v.cos()).add(1);
pDot[5] = pDot[5].add(n.multiply(ksi).multiply(ksi).divide(oMe2.multiply(oMe2.sqrt())));
break;
default :
throw new OrekitInternalError(null);
}
}
/** Returns a string representation of this Keplerian parameters object.
* @return a string representation of this object
*/
public String toString() {
return new StringBuffer().append("Keplerian parameters: ").append('{').
append("a: ").append(a.getReal()).
append("; e: ").append(e.getReal()).
append("; i: ").append(FastMath.toDegrees(i.getReal())).
append("; pa: ").append(FastMath.toDegrees(pa.getReal())).
append("; raan: ").append(FastMath.toDegrees(raan.getReal())).
append("; v: ").append(FastMath.toDegrees(v.getReal())).
append(";}").toString();
}
/**
* Normalize an angle in a 2π wide interval around a center value.
* <p>This method has three main uses:</p>
* <ul>
* <li>normalize an angle between 0 and 2π:<br/>
* {@code a = MathUtils.normalizeAngle(a, FastMath.PI);}</li>
* <li>normalize an angle between -π and +π<br/>
* {@code a = MathUtils.normalizeAngle(a, 0.0);}</li>
* <li>compute the angle between two defining angular positions:<br>
* {@code angle = MathUtils.normalizeAngle(end, start) - start;}</li>
* </ul>
* <p>Note that due to numerical accuracy and since π cannot be represented
* exactly, the result interval is <em>closed</em>, it cannot be half-closed
* as would be more satisfactory in a purely mathematical view.</p>
* @param a angle to normalize
* @param center center of the desired 2π interval for the result
* @param <T> the type of the field elements
* @return a-2kπ with integer k and center-π <= a-2kπ <= center+π
*/
public static <T extends RealFieldElement<T>> T normalizeAngle(final T a, final T center) {
return a.subtract(2 * FastMath.PI * FastMath.floor((a.getReal() + FastMath.PI - center.getReal()) / (2 * FastMath.PI)));
}
@Override
public KeplerianOrbit toOrbit() {
if (hasDerivatives()) {
return new KeplerianOrbit(a.getReal(), e.getReal(), i.getReal(),
pa.getReal(), raan.getReal(), v.getReal(),
aDot.getReal(), eDot.getReal(), iDot.getReal(),
paDot.getReal(), raanDot.getReal(), vDot.getReal(),
PositionAngle.TRUE,
getFrame(), getDate().toAbsoluteDate(), getMu());
} else {
return new KeplerianOrbit(a.getReal(), e.getReal(), i.getReal(),
pa.getReal(), raan.getReal(), v.getReal(),
PositionAngle.TRUE,
getFrame(), getDate().toAbsoluteDate(), getMu());
}
}
}