FieldCartesianOrbit.java
/* Copyright 2002-2020 CS GROUP
* Licensed to CS GROUP (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.Arrays;
import java.util.stream.Stream;
import org.hipparchus.Field;
import org.hipparchus.RealFieldElement;
import org.hipparchus.analysis.differentiation.FieldUnivariateDerivative2;
import org.hipparchus.exception.LocalizedCoreFormats;
import org.hipparchus.exception.MathIllegalStateException;
import org.hipparchus.geometry.euclidean.threed.FieldRotation;
import org.hipparchus.geometry.euclidean.threed.FieldVector3D;
import org.hipparchus.geometry.euclidean.threed.RotationConvention;
import org.hipparchus.geometry.euclidean.threed.Vector3D;
import org.hipparchus.util.FastMath;
import org.hipparchus.util.FieldSinCos;
import org.hipparchus.util.MathArrays;
import org.orekit.errors.OrekitMessages;
import org.orekit.frames.Frame;
import org.orekit.time.AbsoluteDate;
import org.orekit.time.FieldAbsoluteDate;
import org.orekit.utils.CartesianDerivativesFilter;
import org.orekit.utils.FieldPVCoordinates;
import org.orekit.utils.PVCoordinates;
import org.orekit.utils.TimeStampedFieldPVCoordinates;
/** This class holds Cartesian orbital parameters.
* <p>
* The parameters used internally are the Cartesian coordinates:
* <ul>
* <li>x</li>
* <li>y</li>
* <li>z</li>
* <li>xDot</li>
* <li>yDot</li>
* <li>zDot</li>
* </ul>
* contained in {@link PVCoordinates}.
* <p>
* Note that the implementation of this class delegates all non-Cartesian related
* computations ({@link #getA()}, {@link #getEquinoctialEx()}, ...) to an underlying
* instance of the {@link EquinoctialOrbit} class. This implies that using this class
* only for analytical computations which are always based on non-Cartesian
* parameters is perfectly possible but somewhat sub-optimal.
* </p>
* <p>
* The instance <code>CartesianOrbit</code> is guaranteed to be immutable.
* </p>
* @see Orbit
* @see KeplerianOrbit
* @see CircularOrbit
* @see EquinoctialOrbit
* @author Luc Maisonobe
* @author Guylaine Prat
* @author Fabien Maussion
* @author Véronique Pommier-Maurussane
* @since 9.0
*/
public class FieldCartesianOrbit<T extends RealFieldElement<T>> extends FieldOrbit<T> {
/** Indicator for non-Keplerian acceleration. */
private final transient boolean hasNonKeplerianAcceleration;
/** Underlying equinoctial orbit to which high-level methods are delegated. */
private transient FieldEquinoctialOrbit<T> equinoctial;
/** Field used by this class.*/
private final Field<T> field;
/** Zero. (could be usefull)*/
private final T zero;
/** One. (could be useful)*/
private final T one;
/** Constructor from Cartesian parameters.
*
* <p> The acceleration provided in {@code pvCoordinates} 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 pvaCoordinates the position, velocity and acceleration of the satellite.
* @param frame the frame in which the {@link PVCoordinates} are defined
* (<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 FieldCartesianOrbit(final TimeStampedFieldPVCoordinates<T> pvaCoordinates,
final Frame frame, final T mu)
throws IllegalArgumentException {
super(pvaCoordinates, frame, mu);
hasNonKeplerianAcceleration = hasNonKeplerianAcceleration(pvaCoordinates, mu);
equinoctial = null;
field = pvaCoordinates.getPosition().getX().getField();
zero = field.getZero();
one = field.getOne();
}
/** Constructor from Cartesian parameters.
*
* <p> The acceleration provided in {@code pvCoordinates} 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 pvaCoordinates the position and velocity of the satellite.
* @param frame the frame in which the {@link PVCoordinates} 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}
*/
public FieldCartesianOrbit(final FieldPVCoordinates<T> pvaCoordinates, final Frame frame,
final FieldAbsoluteDate<T> date, final T mu)
throws IllegalArgumentException {
this(new TimeStampedFieldPVCoordinates<>(date, pvaCoordinates), frame, mu);
}
/** Constructor from any kind of orbital parameters.
* @param op orbital parameters to copy
*/
public FieldCartesianOrbit(final FieldOrbit<T> op) {
super(op.getPVCoordinates(), op.getFrame(), op.getMu());
hasNonKeplerianAcceleration = op.hasDerivatives();
if (op instanceof FieldEquinoctialOrbit) {
equinoctial = (FieldEquinoctialOrbit<T>) op;
} else if (op instanceof FieldCartesianOrbit) {
equinoctial = ((FieldCartesianOrbit<T>) op).equinoctial;
} else {
equinoctial = null;
}
field = op.getA().getField();
zero = field.getZero();
one = field.getOne();
}
/** {@inheritDoc} */
public OrbitType getType() {
return OrbitType.CARTESIAN;
}
/** Lazy evaluation of equinoctial parameters. */
private void initEquinoctial() {
if (equinoctial == null) {
if (hasDerivatives()) {
// getPVCoordinates includes accelerations that will be interpreted as derivatives
equinoctial = new FieldEquinoctialOrbit<>(getPVCoordinates(), getFrame(), getDate(), getMu());
} else {
// get rid of Keplerian acceleration so we don't assume
// we have derivatives when in fact we don't have them
equinoctial = new FieldEquinoctialOrbit<>(new FieldPVCoordinates<>(getPVCoordinates().getPosition(),
getPVCoordinates().getVelocity()),
getFrame(), getDate(), getMu());
}
}
}
/** Get the position/velocity with derivatives.
* @return position/velocity with derivatives
* @since 10.2
*/
private FieldPVCoordinates<FieldUnivariateDerivative2<T>> getPVDerivatives() {
// PVA coordinates
final FieldPVCoordinates<T> pva = getPVCoordinates();
final FieldVector3D<T> p = pva.getPosition();
final FieldVector3D<T> v = pva.getVelocity();
final FieldVector3D<T> a = pva.getAcceleration();
// Field coordinates
final FieldVector3D<FieldUnivariateDerivative2<T>> pG = new FieldVector3D<>(new FieldUnivariateDerivative2<>(p.getX(), v.getX(), a.getX()),
new FieldUnivariateDerivative2<>(p.getY(), v.getY(), a.getY()),
new FieldUnivariateDerivative2<>(p.getZ(), v.getZ(), a.getZ()));
final FieldVector3D<FieldUnivariateDerivative2<T>> vG = new FieldVector3D<>(new FieldUnivariateDerivative2<>(v.getX(), a.getX(), zero),
new FieldUnivariateDerivative2<>(v.getY(), a.getY(), zero),
new FieldUnivariateDerivative2<>(v.getZ(), a.getZ(), zero));
return new FieldPVCoordinates<>(pG, vG);
}
/** {@inheritDoc} */
public T getA() {
// lazy evaluation of semi-major axis
final T r = getPVCoordinates().getPosition().getNorm();
final T V2 = getPVCoordinates().getVelocity().getNormSq();
return r.divide(r.negate().multiply(V2).divide(getMu()).add(2));
}
/** {@inheritDoc} */
public T getADot() {
if (hasDerivatives()) {
final FieldPVCoordinates<FieldUnivariateDerivative2<T>> pv = getPVDerivatives();
final FieldUnivariateDerivative2<T> r = pv.getPosition().getNorm();
final FieldUnivariateDerivative2<T> V2 = pv.getVelocity().getNormSq();
final FieldUnivariateDerivative2<T> a = r.divide(r.multiply(V2).divide(getMu()).subtract(2).negate());
return a.getDerivative(1);
} else {
return null;
}
}
/** {@inheritDoc} */
public T getE() {
final T muA = getA().multiply(getMu());
if (muA.getReal() > 0) {
// elliptic or circular orbit
final FieldVector3D<T> pvP = getPVCoordinates().getPosition();
final FieldVector3D<T> pvV = getPVCoordinates().getVelocity();
final T rV2OnMu = pvP.getNorm().multiply(pvV.getNormSq()).divide(getMu());
final T eSE = FieldVector3D.dotProduct(pvP, pvV).divide(muA.sqrt());
final T eCE = rV2OnMu.subtract(1);
return (eCE.multiply(eCE).add(eSE.multiply(eSE))).sqrt();
} else {
// hyperbolic orbit
final FieldVector3D<T> pvM = getPVCoordinates().getMomentum();
return pvM.getNormSq().divide(muA).negate().add(1).sqrt();
}
}
/** {@inheritDoc} */
public T getEDot() {
if (hasDerivatives()) {
final FieldPVCoordinates<FieldUnivariateDerivative2<T>> pv = getPVDerivatives();
final FieldUnivariateDerivative2<T> r = pv.getPosition().getNorm();
final FieldUnivariateDerivative2<T> V2 = pv.getVelocity().getNormSq();
final FieldUnivariateDerivative2<T> rV2OnMu = r.multiply(V2).divide(getMu());
final FieldUnivariateDerivative2<T> a = r.divide(rV2OnMu.negate().add(2));
final FieldUnivariateDerivative2<T> eSE = FieldVector3D.dotProduct(pv.getPosition(), pv.getVelocity()).divide(a.multiply(getMu()).sqrt());
final FieldUnivariateDerivative2<T> eCE = rV2OnMu.subtract(1);
final FieldUnivariateDerivative2<T> e = eCE.multiply(eCE).add(eSE.multiply(eSE)).sqrt();
return e.getDerivative(1);
} else {
return null;
}
}
/** {@inheritDoc} */
public T getI() {
return FieldVector3D.angle(new FieldVector3D<>(zero, zero, one), getPVCoordinates().getMomentum());
}
/** {@inheritDoc} */
public T getIDot() {
if (hasDerivatives()) {
final FieldPVCoordinates<FieldUnivariateDerivative2<T>> pv = getPVDerivatives();
final FieldVector3D<FieldUnivariateDerivative2<T>> momentum =
FieldVector3D.crossProduct(pv.getPosition(), pv.getVelocity());
final FieldUnivariateDerivative2<T> i = FieldVector3D.angle(Vector3D.PLUS_K, momentum);
return i.getDerivative(1);
} else {
return null;
}
}
/** {@inheritDoc} */
public T getEquinoctialEx() {
initEquinoctial();
return equinoctial.getEquinoctialEx();
}
/** {@inheritDoc} */
public T getEquinoctialExDot() {
initEquinoctial();
return equinoctial.getEquinoctialExDot();
}
/** {@inheritDoc} */
public T getEquinoctialEy() {
initEquinoctial();
return equinoctial.getEquinoctialEy();
}
/** {@inheritDoc} */
public T getEquinoctialEyDot() {
initEquinoctial();
return equinoctial.getEquinoctialEyDot();
}
/** {@inheritDoc} */
public T getHx() {
final FieldVector3D<T> w = getPVCoordinates().getMomentum().normalize();
// Check for equatorial retrograde orbit
final double x = w.getX().getReal();
final double y = w.getY().getReal();
final double z = w.getZ().getReal();
if (((x * x + y * y) == 0) && z < 0) {
return zero.add(Double.NaN);
}
return w.getY().negate().divide(w.getZ().add(1));
}
/** {@inheritDoc} */
public T getHxDot() {
if (hasDerivatives()) {
final FieldPVCoordinates<FieldUnivariateDerivative2<T>> pv = getPVDerivatives();
final FieldVector3D<FieldUnivariateDerivative2<T>> w =
FieldVector3D.crossProduct(pv.getPosition(), pv.getVelocity()).normalize();
// Check for equatorial retrograde orbit
final double x = w.getX().getValue().getReal();
final double y = w.getY().getValue().getReal();
final double z = w.getZ().getValue().getReal();
if (((x * x + y * y) == 0) && z < 0) {
return zero.add(Double.NaN);
}
final FieldUnivariateDerivative2<T> hx = w.getY().negate().divide(w.getZ().add(1));
return hx.getDerivative(1);
} else {
return null;
}
}
/** {@inheritDoc} */
public T getHy() {
final FieldVector3D<T> w = getPVCoordinates().getMomentum().normalize();
// Check for equatorial retrograde orbit
final double x = w.getX().getReal();
final double y = w.getY().getReal();
final double z = w.getZ().getReal();
if (((x * x + y * y) == 0) && z < 0) {
return zero.add(Double.NaN);
}
return w.getX().divide(w.getZ().add(1));
}
/** {@inheritDoc} */
public T getHyDot() {
if (hasDerivatives()) {
final FieldPVCoordinates<FieldUnivariateDerivative2<T>> pv = getPVDerivatives();
final FieldVector3D<FieldUnivariateDerivative2<T>> w =
FieldVector3D.crossProduct(pv.getPosition(), pv.getVelocity()).normalize();
// Check for equatorial retrograde orbit
final double x = w.getX().getValue().getReal();
final double y = w.getY().getValue().getReal();
final double z = w.getZ().getValue().getReal();
if (((x * x + y * y) == 0) && z < 0) {
return zero.add(Double.NaN);
}
final FieldUnivariateDerivative2<T> hy = w.getX().divide(w.getZ().add(1));
return hy.getDerivative(1);
} else {
return null;
}
}
/** {@inheritDoc} */
public T getLv() {
initEquinoctial();
return equinoctial.getLv();
}
/** {@inheritDoc} */
public T getLvDot() {
initEquinoctial();
return equinoctial.getLvDot();
}
/** {@inheritDoc} */
public T getLE() {
initEquinoctial();
return equinoctial.getLE();
}
/** {@inheritDoc} */
public T getLEDot() {
initEquinoctial();
return equinoctial.getLEDot();
}
/** {@inheritDoc} */
public T getLM() {
initEquinoctial();
return equinoctial.getLM();
}
/** {@inheritDoc} */
public T getLMDot() {
initEquinoctial();
return equinoctial.getLMDot();
}
/** {@inheritDoc} */
public boolean hasDerivatives() {
return hasNonKeplerianAcceleration;
}
/** {@inheritDoc} */
protected TimeStampedFieldPVCoordinates<T> initPVCoordinates() {
// nothing to do here, as the canonical elements are already the Cartesian ones
return getPVCoordinates();
}
/** {@inheritDoc} */
public FieldCartesianOrbit<T> shiftedBy(final double dt) {
return shiftedBy(getDate().getField().getZero().add(dt));
}
/** {@inheritDoc} */
public FieldCartesianOrbit<T> shiftedBy(final T dt) {
final FieldPVCoordinates<T> shiftedPV = (getA().getReal() < 0) ? shiftPVHyperbolic(dt) : shiftPVElliptic(dt);
return new FieldCartesianOrbit<>(shiftedPV, getFrame(), getDate().shiftedBy(dt), getMu());
}
/** {@inheritDoc}
* <p>
* The interpolated instance is created by polynomial Hermite interpolation
* ensuring velocity remains the exact derivative of position.
* </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 FieldCartesianOrbit<T> interpolate(final FieldAbsoluteDate<T> date, final Stream<FieldOrbit<T>> sample) {
final TimeStampedFieldPVCoordinates<T> interpolated =
TimeStampedFieldPVCoordinates.interpolate(date, CartesianDerivativesFilter.USE_PVA,
sample.map(orbit -> orbit.getPVCoordinates()));
return new FieldCartesianOrbit<>(interpolated, getFrame(), date, getMu());
}
/** Compute shifted position and velocity in elliptic case.
* @param dt time shift
* @return shifted position and velocity
*/
private FieldPVCoordinates<T> shiftPVElliptic(final T dt) {
// preliminary computation
final FieldVector3D<T> pvP = getPVCoordinates().getPosition();
final FieldVector3D<T> pvV = getPVCoordinates().getVelocity();
final T r2 = pvP.getNormSq();
final T r = r2.sqrt();
final T rV2OnMu = r.multiply(pvV.getNormSq()).divide(getMu());
final T a = r.divide(rV2OnMu.negate().add(2));
final T eSE = FieldVector3D.dotProduct(pvP, pvV).divide(a.multiply(getMu()).sqrt());
final T eCE = rV2OnMu.subtract(1);
final T e2 = eCE.multiply(eCE).add(eSE.multiply(eSE));
// we can use any arbitrary reference 2D frame in the orbital plane
// in order to simplify some equations below, we use the current position as the u axis
final FieldVector3D<T> u = pvP.normalize();
final FieldVector3D<T> v = FieldVector3D.crossProduct(FieldVector3D.crossProduct(pvP, pvV), u).normalize();
// the following equations rely on the specific choice of u explained above,
// some coefficients that vanish to 0 in this case have already been removed here
final T ex = eCE.subtract(e2).multiply(a).divide(r);
final T s = e2.negate().add(1).sqrt();
final T ey = s.negate().multiply(eSE).multiply(a).divide(r);
final T beta = s.add(1).reciprocal();
final T thetaE0 = ey.add(eSE.multiply(beta).multiply(ex)).atan2(r.divide(a).add(ex).subtract(eSE.multiply(beta).multiply(ey)));
final FieldSinCos<T> scThetaE0 = FastMath.sinCos(thetaE0);
final T thetaM0 = thetaE0.subtract(ex.multiply(scThetaE0.sin())).add(ey.multiply(scThetaE0.cos()));
// compute in-plane shifted eccentric argument
final T sqrtMmuOA = a.reciprocal().multiply(getMu()).sqrt();
final T thetaM1 = thetaM0.add(sqrtMmuOA.divide(a).multiply(dt));
final T thetaE1 = meanToEccentric(thetaM1, ex, ey);
final FieldSinCos<T> scTE = FastMath.sinCos(thetaE1);
final T cTE = scTE.cos();
final T sTE = scTE.sin();
// compute shifted in-plane Cartesian coordinates
final T exey = ex.multiply(ey);
final T exCeyS = ex.multiply(cTE).add(ey.multiply(sTE));
final T x = a.multiply(beta.multiply(ey).multiply(ey).negate().add(1).multiply(cTE).add(beta.multiply(exey).multiply(sTE)).subtract(ex));
final T y = a.multiply(beta.multiply(ex).multiply(ex).negate().add(1).multiply(sTE).add(beta.multiply(exey).multiply(cTE)).subtract(ey));
final T factor = sqrtMmuOA.divide(exCeyS.negate().add(1));
final T xDot = factor.multiply(beta.multiply(ey).multiply(exCeyS).subtract(sTE));
final T yDot = factor.multiply(cTE.subtract(beta.multiply(ex).multiply(exCeyS)));
final FieldVector3D<T> shiftedP = new FieldVector3D<>(x, u, y, v);
final FieldVector3D<T> shiftedV = new FieldVector3D<>(xDot, u, yDot, v);
if (hasNonKeplerianAcceleration) {
// extract non-Keplerian part of the initial acceleration
final FieldVector3D<T> nonKeplerianAcceleration = new FieldVector3D<>(one, getPVCoordinates().getAcceleration(),
r.multiply(r2).reciprocal().multiply(getMu()), pvP);
// add the quadratic motion due to the non-Keplerian acceleration to the Keplerian motion
final FieldVector3D<T> fixedP = new FieldVector3D<>(one, shiftedP,
dt.multiply(dt).multiply(0.5), nonKeplerianAcceleration);
final T fixedR2 = fixedP.getNormSq();
final T fixedR = fixedR2.sqrt();
final FieldVector3D<T> fixedV = new FieldVector3D<>(one, shiftedV,
dt, nonKeplerianAcceleration);
final FieldVector3D<T> fixedA = new FieldVector3D<>(fixedR.multiply(fixedR2).reciprocal().multiply(getMu().negate()), shiftedP,
one, nonKeplerianAcceleration);
return new FieldPVCoordinates<>(fixedP, fixedV, fixedA);
} else {
// don't include acceleration,
// so the shifted orbit is not considered to have derivatives
return new FieldPVCoordinates<>(shiftedP, shiftedV);
}
}
/** Compute shifted position and velocity in hyperbolic case.
* @param dt time shift
* @return shifted position and velocity
*/
private FieldPVCoordinates<T> shiftPVHyperbolic(final T dt) {
final FieldPVCoordinates<T> pv = getPVCoordinates();
final FieldVector3D<T> pvP = pv.getPosition();
final FieldVector3D<T> pvV = pv.getVelocity();
final FieldVector3D<T> pvM = pv.getMomentum();
final T r2 = pvP.getNormSq();
final T r = r2.sqrt();
final T rV2OnMu = r.multiply(pvV.getNormSq()).divide(getMu());
final T a = getA();
final T muA = a.multiply(getMu());
final T e = one.subtract(FieldVector3D.dotProduct(pvM, pvM).divide(muA)).sqrt();
final T sqrt = e.add(1).divide(e.subtract(1)).sqrt();
// compute mean anomaly
final T eSH = FieldVector3D.dotProduct(pvP, pvV).divide(muA.negate().sqrt());
final T eCH = rV2OnMu.subtract(1);
final T H0 = eCH.add(eSH).divide(eCH.subtract(eSH)).log().divide(2);
final T M0 = e.multiply(H0.sinh()).subtract(H0);
// find canonical 2D frame with p pointing to perigee
final T v0 = sqrt.multiply(H0.divide(2).tanh()).atan().multiply(2);
final FieldVector3D<T> p = new FieldRotation<>(pvM, v0, RotationConvention.FRAME_TRANSFORM).applyTo(pvP).normalize();
final FieldVector3D<T> q = FieldVector3D.crossProduct(pvM, p).normalize();
// compute shifted eccentric anomaly
final T M1 = M0.add(getKeplerianMeanMotion().multiply(dt));
final T H1 = meanToHyperbolicEccentric(M1, e);
// compute shifted in-plane Cartesian coordinates
final T cH = H1.cosh();
final T sH = H1.sinh();
final T sE2m1 = e.subtract(1).multiply(e.add(1)).sqrt();
// coordinates of position and velocity in the orbital plane
final T x = a.multiply(cH.subtract(e));
final T y = a.negate().multiply(sE2m1).multiply(sH);
final T factor = getMu().divide(a.negate()).sqrt().divide(e.multiply(cH).subtract(1));
final T xDot = factor.negate().multiply(sH);
final T yDot = factor.multiply(sE2m1).multiply(cH);
final FieldVector3D<T> shiftedP = new FieldVector3D<>(x, p, y, q);
final FieldVector3D<T> shiftedV = new FieldVector3D<>(xDot, p, yDot, q);
if (hasNonKeplerianAcceleration) {
// extract non-Keplerian part of the initial acceleration
final FieldVector3D<T> nonKeplerianAcceleration = new FieldVector3D<>(one, getPVCoordinates().getAcceleration(),
r.multiply(r2).reciprocal().multiply(getMu()), pvP);
// add the quadratic motion due to the non-Keplerian acceleration to the Keplerian motion
final FieldVector3D<T> fixedP = new FieldVector3D<>(one, shiftedP,
dt.multiply(dt).multiply(0.5), nonKeplerianAcceleration);
final T fixedR2 = fixedP.getNormSq();
final T fixedR = fixedR2.sqrt();
final FieldVector3D<T> fixedV = new FieldVector3D<>(one, shiftedV,
dt, nonKeplerianAcceleration);
final FieldVector3D<T> fixedA = new FieldVector3D<>(fixedR.multiply(fixedR2).reciprocal().multiply(getMu().negate()), shiftedP,
one, nonKeplerianAcceleration);
return new FieldPVCoordinates<>(fixedP, fixedV, fixedA);
} else {
// don't include acceleration,
// so the shifted orbit is not considered to have derivatives
return new FieldPVCoordinates<>(shiftedP, shiftedV);
}
}
/** Computes the eccentric in-plane argument from the mean in-plane argument.
* @param thetaM = mean in-plane argument (rad)
* @param ex first component of eccentricity vector
* @param ey second component of eccentricity vector
* @return the eccentric in-plane argument.
*/
private T meanToEccentric(final T thetaM, final T ex, final T ey) {
// Generalization of Kepler equation to in-plane parameters
// with thetaE = eta + E and
// thetaM = eta + M = thetaE - ex.sin(thetaE) + ey.cos(thetaE)
// and eta being counted from an arbitrary reference in the orbital plane
T thetaE = thetaM;
T thetaEMthetaM = zero;
int iter = 0;
do {
final FieldSinCos<T> scThetaE = FastMath.sinCos(thetaE);
final T f2 = ex.multiply(scThetaE.sin()).subtract(ey.multiply(scThetaE.cos()));
final T f1 = one.subtract(ex.multiply(scThetaE.cos())).subtract(ey.multiply(scThetaE.sin()));
final T f0 = thetaEMthetaM.subtract(f2);
final T f12 = f1.multiply(2.0);
final T shift = f0.multiply(f12).divide(f1.multiply(f12).subtract(f0.multiply(f2)));
thetaEMthetaM = thetaEMthetaM.subtract(shift);
thetaE = thetaM.add(thetaEMthetaM);
if (FastMath.abs(shift.getReal()) <= 1.0e-12) {
return thetaE;
}
} while (++iter < 50);
throw new MathIllegalStateException(LocalizedCoreFormats.CONVERGENCE_FAILED);
}
/** 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 ecc eccentricity
* @return the hyperbolic eccentric anomaly
*/
private T meanToHyperbolicEccentric(final T M, final T ecc) {
// Resolution of hyperbolic Kepler equation for Keplerian parameters
// Initial guess
T H;
if (ecc.getReal() < 1.6) {
if ((-FastMath.PI < M.getReal() && M.getReal() < 0.) || M.getReal() > FastMath.PI) {
H = M.subtract(ecc);
} else {
H = M.add(ecc);
}
} else {
if (ecc.getReal() < 3.6 && FastMath.abs(M.getReal()) > FastMath.PI) {
H = M.subtract(ecc.copySign(M));
} else {
H = M.divide(ecc.subtract(1.));
}
}
// Iterative computation
int iter = 0;
do {
final T f3 = ecc.multiply(H.cosh());
final T f2 = ecc.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 (FastMath.abs(shift.getReal()) <= 1.0e-12) {
return H;
}
} while (++iter < 50);
throw new MathIllegalStateException(OrekitMessages.UNABLE_TO_COMPUTE_HYPERBOLIC_ECCENTRIC_ANOMALY,
iter);
}
/** Create a 6x6 identity matrix.
* @return 6x6 identity matrix
*/
private T[][] create6x6Identity() {
// this is the fastest way to set the 6x6 identity matrix
final T[][] identity = MathArrays.buildArray(field, 6, 6);
for (int i = 0; i < 6; i++) {
Arrays.fill(identity[i], zero);
identity[i][i] = one;
}
return identity;
}
@Override
protected T[][] computeJacobianMeanWrtCartesian() {
return create6x6Identity();
}
@Override
protected T[][] computeJacobianEccentricWrtCartesian() {
return create6x6Identity();
}
@Override
protected T[][] computeJacobianTrueWrtCartesian() {
return create6x6Identity();
}
/** {@inheritDoc} */
public void addKeplerContribution(final PositionAngle type, final T gm,
final T[] pDot) {
final FieldPVCoordinates<T> pv = getPVCoordinates();
// position derivative is velocity
final FieldVector3D<T> velocity = pv.getVelocity();
pDot[0] = pDot[0].add(velocity.getX());
pDot[1] = pDot[1].add(velocity.getY());
pDot[2] = pDot[2].add(velocity.getZ());
// velocity derivative is Newtonian acceleration
final FieldVector3D<T> position = pv.getPosition();
final T r2 = position.getNormSq();
final T coeff = r2.multiply(r2.sqrt()).reciprocal().negate().multiply(gm);
pDot[3] = pDot[3].add(coeff.multiply(position.getX()));
pDot[4] = pDot[4].add(coeff.multiply(position.getY()));
pDot[5] = pDot[5].add(coeff.multiply(position.getZ()));
}
/** Returns a string representation of this Orbit object.
* @return a string representation of this object
*/
public String toString() {
// use only the six defining elements, like the other Orbit.toString() methods
final String comma = ", ";
final PVCoordinates pv = getPVCoordinates().toPVCoordinates();
final Vector3D p = pv.getPosition();
final Vector3D v = pv.getVelocity();
return "Cartesian parameters: {P(" +
p.getX() + comma +
p.getY() + comma +
p.getZ() + "), V(" +
v.getX() + comma +
v.getY() + comma +
v.getZ() + ")}";
}
@Override
public CartesianOrbit toOrbit() {
final PVCoordinates pv = getPVCoordinates().toPVCoordinates();
final AbsoluteDate date = getPVCoordinates().getDate().toAbsoluteDate();
if (hasDerivatives()) {
// getPVCoordinates includes accelerations that will be interpreted as derivatives
return new CartesianOrbit(pv, getFrame(), date, getMu().getReal());
} else {
// get rid of Keplerian acceleration so we don't assume
// we have derivatives when in fact we don't have them
return new CartesianOrbit(new PVCoordinates(pv.getPosition(), pv.getVelocity()),
getFrame(), date, getMu().getReal());
}
}
}