FieldEquinoctialOrbit.java
/* Copyright 2002-2022 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,
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package org.orekit.orbits;
import java.util.List;
import java.util.stream.Collectors;
import java.util.stream.Stream;
import org.hipparchus.Field;
import org.hipparchus.CalculusFieldElement;
import org.hipparchus.analysis.differentiation.FieldUnivariateDerivative1;
import org.hipparchus.analysis.interpolation.FieldHermiteInterpolator;
import org.hipparchus.geometry.euclidean.threed.FieldVector3D;
import org.hipparchus.util.FastMath;
import org.hipparchus.util.FieldSinCos;
import org.hipparchus.util.MathArrays;
import org.hipparchus.util.MathUtils;
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 equinoctial orbital parameters, which can support both
* circular and equatorial orbits.
* <p>
* The parameters used internally are the equinoctial elements which can be
* related to Keplerian elements as follows:
* <pre>
* a
* ex = e cos(ω + Ω)
* ey = e sin(ω + Ω)
* hx = tan(i/2) cos(Ω)
* hy = tan(i/2) sin(Ω)
* lv = v + ω + Ω
* </pre>
* where ω stands for the Perigee Argument and Ω stands for the
* Right Ascension of the Ascending Node.
* <p>
* The conversion equations from and to Keplerian elements given above hold only
* when both sides are unambiguously defined, i.e. when orbit is neither equatorial
* nor circular. When orbit is either equatorial or circular, the equinoctial
* parameters are still unambiguously defined whereas some Keplerian elements
* (more precisely ω and Ω) become ambiguous. For this reason, equinoctial
* parameters are the recommended way to represent orbits.
* </p>
* <p>
* The instance <code>EquinoctialOrbit</code> is guaranteed to be immutable.
* </p>
* @see Orbit
* @see KeplerianOrbit
* @see CircularOrbit
* @see CartesianOrbit
* @author Mathieu Roméro
* @author Luc Maisonobe
* @author Guylaine Prat
* @author Fabien Maussion
* @author Véronique Pommier-Maurussane
* @since 9.0
*/
public class FieldEquinoctialOrbit<T extends CalculusFieldElement<T>> extends FieldOrbit<T> {
/** Semi-major axis (m). */
private final T a;
/** First component of the eccentricity vector. */
private final T ex;
/** Second component of the eccentricity vector. */
private final T ey;
/** First component of the inclination vector. */
private final T hx;
/** Second component of the inclination vector. */
private final T hy;
/** True longitude argument (rad). */
private final T lv;
/** Semi-major axis derivative (m/s). */
private final T aDot;
/** First component of the eccentricity vector derivative. */
private final T exDot;
/** Second component of the eccentricity vector derivative. */
private final T eyDot;
/** First component of the inclination vector derivative. */
private final T hxDot;
/** Second component of the inclination vector derivative. */
private final T hyDot;
/** True longitude argument derivative (rad/s). */
private final T lvDot;
/** Partial Cartesian coordinates (position and velocity are valid, acceleration may be missing). */
private FieldPVCoordinates<T> partialPV;
/** Field used by this class.*/
private Field<T> field;
/**Zero.*/
private T zero;
/**One.*/
private T one;
/** Creates a new instance.
* @param a semi-major axis (m)
* @param ex e cos(ω + Ω), first component of eccentricity vector
* @param ey e sin(ω + Ω), second component of eccentricity vector
* @param hx tan(i/2) cos(Ω), first component of inclination vector
* @param hy tan(i/2) sin(Ω), second component of inclination vector
* @param l (M or E or v) + ω + Ω, mean, eccentric or true longitude argument (rad)
* @param type type of longitude argument
* @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 eccentricity is equal to 1 or larger or
* if frame is not a {@link Frame#isPseudoInertial pseudo-inertial frame}
*/
public FieldEquinoctialOrbit(final T a, final T ex, final T ey,
final T hx, final T hy, final T l,
final PositionAngle type,
final Frame frame, final FieldAbsoluteDate<T> date, final T mu)
throws IllegalArgumentException {
this(a, ex, ey, hx, hy, l,
null, null, null, null, null, null,
type, frame, date, mu);
}
/** Creates a new instance.
* @param a semi-major axis (m)
* @param ex e cos(ω + Ω), first component of eccentricity vector
* @param ey e sin(ω + Ω), second component of eccentricity vector
* @param hx tan(i/2) cos(Ω), first component of inclination vector
* @param hy tan(i/2) sin(Ω), second component of inclination vector
* @param l (M or E or v) + ω + Ω, mean, eccentric or true longitude argument (rad)
* @param aDot semi-major axis derivative (m/s)
* @param exDot d(e cos(ω + Ω))/dt, first component of eccentricity vector derivative
* @param eyDot d(e sin(ω + Ω))/dt, second component of eccentricity vector derivative
* @param hxDot d(tan(i/2) cos(Ω))/dt, first component of inclination vector derivative
* @param hyDot d(tan(i/2) sin(Ω))/dt, second component of inclination vector derivative
* @param lDot d(M or E or v) + ω + Ω)/dr, mean, eccentric or true longitude argument derivative (rad/s)
* @param type type of longitude argument
* @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 eccentricity is equal to 1 or larger or
* if frame is not a {@link Frame#isPseudoInertial pseudo-inertial frame}
*/
public FieldEquinoctialOrbit(final T a, final T ex, final T ey,
final T hx, final T hy, final T l,
final T aDot, final T exDot, final T eyDot,
final T hxDot, final T hyDot, final T lDot,
final PositionAngle type,
final Frame frame, final FieldAbsoluteDate<T> date, final T mu)
throws IllegalArgumentException {
super(frame, date, mu);
field = a.getField();
zero = field.getZero();
one = field.getOne();
if (ex.getReal() * ex.getReal() + ey.getReal() * ey.getReal() >= 1.0) {
throw new OrekitIllegalArgumentException(OrekitMessages.HYPERBOLIC_ORBIT_NOT_HANDLED_AS,
getClass().getName());
}
this.a = a;
this.aDot = aDot;
this.ex = ex;
this.exDot = exDot;
this.ey = ey;
this.eyDot = eyDot;
this.hx = hx;
this.hxDot = hxDot;
this.hy = hy;
this.hyDot = hyDot;
if (hasDerivatives()) {
final FieldUnivariateDerivative1<T> exUD = new FieldUnivariateDerivative1<>(ex, exDot);
final FieldUnivariateDerivative1<T> eyUD = new FieldUnivariateDerivative1<>(ey, eyDot);
final FieldUnivariateDerivative1<T> lUD = new FieldUnivariateDerivative1<>(l, lDot);
final FieldUnivariateDerivative1<T> lvUD;
switch (type) {
case MEAN :
lvUD = eccentricToTrue(meanToEccentric(lUD, exUD, eyUD), exUD, eyUD);
break;
case ECCENTRIC :
lvUD = eccentricToTrue(lUD, exUD, eyUD);
break;
case TRUE :
lvUD = lUD;
break;
default : // this should never happen
throw new OrekitInternalError(null);
}
this.lv = lvUD.getValue();
this.lvDot = lvUD.getDerivative(1);
} else {
switch (type) {
case MEAN :
this.lv = eccentricToTrue(meanToEccentric(l, ex, ey), ex, ey);
break;
case ECCENTRIC :
this.lv = eccentricToTrue(l, ex, ey);
break;
case TRUE :
this.lv = l;
break;
default :
throw new OrekitInternalError(null);
}
this.lvDot = null;
}
this.partialPV = null;
}
/** 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(CalculusFieldElement)} and {@link #getPVCoordinates(FieldAbsoluteDate, Frame)}.
*
* @param pvCoordinates the position, velocity and acceleration
* @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 eccentricity is equal to 1 or larger or
* if frame is not a {@link Frame#isPseudoInertial pseudo-inertial frame}
*/
public FieldEquinoctialOrbit(final TimeStampedFieldPVCoordinates<T> pvCoordinates,
final Frame frame, final T mu)
throws IllegalArgumentException {
super(pvCoordinates, frame, mu);
field = pvCoordinates.getPosition().getX().getField();
zero = field.getZero();
one = field.getOne();
// compute semi-major axis
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);
if (rV2OnMu.getReal() > 2) {
throw new OrekitIllegalArgumentException(OrekitMessages.HYPERBOLIC_ORBIT_NOT_HANDLED_AS,
getClass().getName());
}
// compute inclination vector
final FieldVector3D<T> w = pvCoordinates.getMomentum().normalize();
final T d = one.divide(one.add(w.getZ()));
hx = d.negate().multiply(w.getY());
hy = d.multiply(w.getX());
// compute true longitude argument
final T cLv = (pvP.getX().subtract(d.multiply(pvP.getZ()).multiply(w.getX()))).divide(r);
final T sLv = (pvP.getY().subtract(d.multiply(pvP.getZ()).multiply(w.getY()))).divide(r);
lv = sLv.atan2(cLv);
// compute semi-major axis
a = r.divide(rV2OnMu.negate().add(2));
// compute eccentricity vector
final T eSE = FieldVector3D.dotProduct(pvP, pvV).divide(a.multiply(mu).sqrt());
final T eCE = rV2OnMu.subtract(1);
final T e2 = eCE.multiply(eCE).add(eSE.multiply(eSE));
final T f = eCE.subtract(e2);
final T g = e2.negate().add(1).sqrt().multiply(eSE);
ex = a.multiply(f.multiply(cLv).add( g.multiply(sLv))).divide(r);
ey = a.multiply(f.multiply(sLv).subtract(g.multiply(cLv))).divide(r);
partialPV = pvCoordinates;
if (hasNonKeplerianAcceleration(pvCoordinates, mu)) {
// 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.negate()), 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));
exDot = jacobian[1][3].multiply(aX).add(jacobian[1][4].multiply(aY)).add(jacobian[1][5].multiply(aZ));
eyDot = jacobian[2][3].multiply(aX).add(jacobian[2][4].multiply(aY)).add(jacobian[2][5].multiply(aZ));
hxDot = jacobian[3][3].multiply(aX).add(jacobian[3][4].multiply(aY)).add(jacobian[3][5].multiply(aZ));
hyDot = 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 lMDot = getKeplerianMeanMotion().
add(jacobian[5][3].multiply(aX)).add(jacobian[5][4].multiply(aY)).add(jacobian[5][5].multiply(aZ));
final FieldUnivariateDerivative1<T> exUD = new FieldUnivariateDerivative1<>(ex, exDot);
final FieldUnivariateDerivative1<T> eyUD = new FieldUnivariateDerivative1<>(ey, eyDot);
final FieldUnivariateDerivative1<T> lMUD = new FieldUnivariateDerivative1<>(getLM(), lMDot);
final FieldUnivariateDerivative1<T> lvUD = eccentricToTrue(meanToEccentric(lMUD, exUD, eyUD), exUD, eyUD);
lvDot = lvUD.getDerivative(1);
} else {
// acceleration is either almost zero or NaN,
// we assume acceleration was not known
// we don't set up derivatives
aDot = null;
exDot = null;
eyDot = null;
hxDot = null;
hyDot = null;
lvDot = null;
}
}
/** 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(CalculusFieldElement)} and {@link #getPVCoordinates(FieldAbsoluteDate, Frame)}.
*
* @param pvCoordinates the position end velocity
* @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 eccentricity is equal to 1 or larger or
* if frame is not a {@link Frame#isPseudoInertial pseudo-inertial frame}
*/
public FieldEquinoctialOrbit(final FieldPVCoordinates<T> pvCoordinates, final Frame frame,
final FieldAbsoluteDate<T> date, final T mu)
throws IllegalArgumentException {
this(new TimeStampedFieldPVCoordinates<>(date, pvCoordinates), frame, mu);
}
/** Constructor from any kind of orbital parameters.
* @param op orbital parameters to copy
*/
public FieldEquinoctialOrbit(final FieldOrbit<T> op) {
super(op.getFrame(), op.getDate(), op.getMu());
a = op.getA();
ex = op.getEquinoctialEx();
ey = op.getEquinoctialEy();
hx = op.getHx();
hy = op.getHy();
lv = op.getLv();
aDot = op.getADot();
exDot = op.getEquinoctialExDot();
eyDot = op.getEquinoctialEyDot();
hxDot = op.getHxDot();
hyDot = op.getHyDot();
lvDot = op.getLvDot();
field = a.getField();
zero = field.getZero();
one = field.getOne();
}
/** {@inheritDoc} */
public OrbitType getType() {
return OrbitType.EQUINOCTIAL;
}
/** {@inheritDoc} */
public T getA() {
return a;
}
/** {@inheritDoc} */
public T getADot() {
return aDot;
}
/** {@inheritDoc} */
public T getEquinoctialEx() {
return ex;
}
/** {@inheritDoc} */
public T getEquinoctialExDot() {
return exDot;
}
/** {@inheritDoc} */
public T getEquinoctialEy() {
return ey;
}
/** {@inheritDoc} */
public T getEquinoctialEyDot() {
return eyDot;
}
/** {@inheritDoc} */
public T getHx() {
return hx;
}
/** {@inheritDoc} */
public T getHxDot() {
return hxDot;
}
/** {@inheritDoc} */
public T getHy() {
return hy;
}
/** {@inheritDoc} */
public T getHyDot() {
return hyDot;
}
/** {@inheritDoc} */
public T getLv() {
return lv;
}
/** {@inheritDoc} */
public T getLvDot() {
return lvDot;
}
/** {@inheritDoc} */
public T getLE() {
return trueToEccentric(lv, ex, ey);
}
/** {@inheritDoc} */
public T getLEDot() {
if (!hasDerivatives()) {
return null;
}
final FieldUnivariateDerivative1<T> lVUD = new FieldUnivariateDerivative1<>(lv, lvDot);
final FieldUnivariateDerivative1<T> exUD = new FieldUnivariateDerivative1<>(ex, exDot);
final FieldUnivariateDerivative1<T> eyUD = new FieldUnivariateDerivative1<>(ey, eyDot);
final FieldUnivariateDerivative1<T> lEUD = trueToEccentric(lVUD, exUD, eyUD);
return lEUD.getDerivative(1);
}
/** {@inheritDoc} */
public T getLM() {
return eccentricToMean(trueToEccentric(lv, ex, ey), ex, ey);
}
/** {@inheritDoc} */
public T getLMDot() {
if (!hasDerivatives()) {
return null;
}
final FieldUnivariateDerivative1<T> lVUD = new FieldUnivariateDerivative1<>(lv, lvDot);
final FieldUnivariateDerivative1<T> exUD = new FieldUnivariateDerivative1<>(ex, exDot);
final FieldUnivariateDerivative1<T> eyUD = new FieldUnivariateDerivative1<>(ey, eyDot);
final FieldUnivariateDerivative1<T> lMUD = eccentricToMean(trueToEccentric(lVUD, exUD, eyUD), exUD, eyUD);
return lMUD.getDerivative(1);
}
/** Get the longitude argument.
* @param type type of the angle
* @return longitude argument (rad)
*/
public T getL(final PositionAngle type) {
return (type == PositionAngle.MEAN) ? getLM() :
((type == PositionAngle.ECCENTRIC) ? getLE() :
getLv());
}
/** Get the longitude argument derivative.
* @param type type of the angle
* @return longitude argument derivative (rad/s)
*/
public T getLDot(final PositionAngle type) {
return (type == PositionAngle.MEAN) ? getLMDot() :
((type == PositionAngle.ECCENTRIC) ? getLEDot() :
getLvDot());
}
/** {@inheritDoc} */
@Override
public boolean hasDerivatives() {
return aDot != null;
}
/** Computes the true longitude argument from the eccentric longitude argument.
* @param lE = E + ω + Ω eccentric longitude argument (rad)
* @param ex first component of the eccentricity vector
* @param ey second component of the eccentricity vector
* @param <T> Type of the field elements
* @return the true longitude argument
*/
public static <T extends CalculusFieldElement<T>> T eccentricToTrue(final T lE, final T ex, final T ey) {
final T epsilon = ex.multiply(ex).add(ey.multiply(ey)).negate().add(1).sqrt();
final FieldSinCos<T> scLE = FastMath.sinCos(lE);
final T cosLE = scLE.cos();
final T sinLE = scLE.sin();
final T num = ex.multiply(sinLE).subtract(ey.multiply(cosLE));
final T den = epsilon.add(1).subtract(ex.multiply(cosLE)).subtract(ey.multiply(sinLE));
return lE.add(num.divide(den).atan().multiply(2));
}
/** Computes the eccentric longitude argument from the true longitude argument.
* @param lv = v + ω + Ω true longitude argument (rad)
* @param ex first component of the eccentricity vector
* @param ey second component of the eccentricity vector
* @param <T> Type of the field elements
* @return the eccentric longitude argument
*/
public static <T extends CalculusFieldElement<T>> T trueToEccentric(final T lv, final T ex, final T ey) {
final T epsilon = ex.multiply(ex).add(ey.multiply(ey)).negate().add(1).sqrt();
final FieldSinCos<T> scLv = FastMath.sinCos(lv);
final T cosLv = scLv.cos();
final T sinLv = scLv.sin();
final T num = ey.multiply(cosLv).subtract(ex.multiply(sinLv));
final T den = epsilon.add(1).add(ex.multiply(cosLv)).add(ey.multiply(sinLv));
return lv.add(num.divide(den).atan().multiply(2));
}
/** Computes the eccentric longitude argument from the mean longitude argument.
* @param lM = M + ω + Ω mean longitude argument (rad)
* @param ex first component of the eccentricity vector
* @param ey second component of the eccentricity vector
* @param <T> Type of the field elements
* @return the eccentric longitude argument
*/
public static <T extends CalculusFieldElement<T>> T meanToEccentric(final T lM, final T ex, final T ey) {
// Generalization of Kepler equation to equinoctial parameters
// with lE = PA + RAAN + E and
// lM = PA + RAAN + M = lE - ex.sin(lE) + ey.cos(lE)
T lE = lM;
T shift = lM.getField().getZero();
T lEmlM = lM.getField().getZero();
FieldSinCos<T> scLE = FastMath.sinCos(lE);
int iter = 0;
do {
final T f2 = ex.multiply(scLE.sin()).subtract(ey.multiply(scLE.cos()));
final T f1 = ex.multiply(scLE.cos()).add(ey.multiply(scLE.sin())).negate().add(1);
final T f0 = lEmlM.subtract(f2);
final T f12 = f1.multiply(2.0);
shift = f0.multiply(f12).divide(f1.multiply(f12).subtract(f0.multiply(f2)));
lEmlM = lEmlM.subtract(shift);
lE = lM.add(lEmlM);
scLE = FastMath.sinCos(lE);
} while (++iter < 50 && FastMath.abs(shift.getReal()) > 1.0e-12);
return lE;
}
/** Computes the mean longitude argument from the eccentric longitude argument.
* @param lE = E + ω + Ω mean longitude argument (rad)
* @param ex first component of the eccentricity vector
* @param ey second component of the eccentricity vector
* @param <T> Type of the field elements
* @return the mean longitude argument
*/
public static <T extends CalculusFieldElement<T>> T eccentricToMean(final T lE, final T ex, final T ey) {
final FieldSinCos<T> scLE = FastMath.sinCos(lE);
return lE.subtract(ex.multiply(scLE.sin())).add(ey.multiply(scLE.cos()));
}
/** {@inheritDoc} */
public T getE() {
return ex.multiply(ex).add(ey.multiply(ey)).sqrt();
}
/** {@inheritDoc} */
public T getEDot() {
if (!hasDerivatives()) {
return null;
}
return ex.multiply(exDot).add(ey.multiply(eyDot)).divide(ex.multiply(ex).add(ey.multiply(ey)).sqrt());
}
/** {@inheritDoc} */
public T getI() {
return hx.multiply(hx).add(hy.multiply(hy)).sqrt().atan().multiply(2);
}
/** {@inheritDoc} */
public T getIDot() {
if (!hasDerivatives()) {
return null;
}
final T h2 = hx.multiply(hx).add(hy.multiply(hy));
final T h = h2.sqrt();
return hx.multiply(hxDot).add(hy.multiply(hyDot)).multiply(2).divide(h.multiply(h2.add(1)));
}
/** Compute position and velocity but not acceleration.
*/
private void computePVWithoutA() {
if (partialPV != null) {
// already computed
return;
}
// get equinoctial parameters
final T lE = getLE();
// inclination-related intermediate parameters
final T hx2 = hx.multiply(hx);
final T hy2 = hy.multiply(hy);
final T factH = one.divide(hx2.add(1.0).add(hy2));
// reference axes defining the orbital plane
final T ux = hx2.add(1.0).subtract(hy2).multiply(factH);
final T uy = hx.multiply(hy).multiply(factH).multiply(2);
final T uz = hy.multiply(-2).multiply(factH);
final T vx = uy;
final T vy = (hy2.subtract(hx2).add(1)).multiply(factH);
final T vz = hx.multiply(factH).multiply(2);
// eccentricity-related intermediate parameters
final T ex2 = ex.multiply(ex);
final T exey = ex.multiply(ey);
final T ey2 = ey.multiply(ey);
final T e2 = ex2.add(ey2);
final T eta = one.subtract(e2).sqrt().add(1);
final T beta = one.divide(eta);
// eccentric longitude argument
final FieldSinCos<T> scLe = FastMath.sinCos(lE);
final T cLe = scLe.cos();
final T sLe = scLe.sin();
final T exCeyS = ex.multiply(cLe).add(ey.multiply(sLe));
// coordinates of position and velocity in the orbital plane
final T x = a.multiply(one.subtract(beta.multiply(ey2)).multiply(cLe).add(beta.multiply(exey).multiply(sLe)).subtract(ex));
final T y = a.multiply(one.subtract(beta.multiply(ex2)).multiply(sLe).add(beta .multiply(exey).multiply(cLe)).subtract(ey));
final T factor = getMu().divide(a).sqrt().divide(one.subtract(exCeyS));
final T xdot = factor.multiply(sLe.negate().add(beta.multiply(ey).multiply(exCeyS)));
final T ydot = factor.multiply(cLe.subtract(beta.multiply(ex).multiply(exCeyS)));
final FieldVector3D<T> position =
new FieldVector3D<>(x.multiply(ux).add(y.multiply(vx)),
x.multiply(uy).add(y.multiply(vy)),
x.multiply(uz).add(y.multiply(vz)));
final FieldVector3D<T> velocity =
new FieldVector3D<>(xdot.multiply(ux).add(ydot.multiply(vx)), xdot.multiply(uy).add(ydot.multiply(vy)), xdot.multiply(uz).add(ydot.multiply(vz)));
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 = getLMDot().subtract(getKeplerianMeanMotion());
final T nonKeplerianAx = dCdP[3][0].multiply(aDot).
add(dCdP[3][1].multiply(exDot)).
add(dCdP[3][2].multiply(eyDot)).
add(dCdP[3][3].multiply(hxDot)).
add(dCdP[3][4].multiply(hyDot)).
add(dCdP[3][5].multiply(nonKeplerianMeanMotion));
final T nonKeplerianAy = dCdP[4][0].multiply(aDot).
add(dCdP[4][1].multiply(exDot)).
add(dCdP[4][2].multiply(eyDot)).
add(dCdP[4][3].multiply(hxDot)).
add(dCdP[4][4].multiply(hyDot)).
add(dCdP[4][5].multiply(nonKeplerianMeanMotion));
final T nonKeplerianAz = dCdP[5][0].multiply(aDot).
add(dCdP[5][1].multiply(exDot)).
add(dCdP[5][2].multiply(eyDot)).
add(dCdP[5][3].multiply(hxDot)).
add(dCdP[5][4].multiply(hyDot)).
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().negate()),
partialPV.getPosition());
final FieldVector3D<T> acceleration = hasDerivatives() ?
keplerianAcceleration.add(nonKeplerianAcceleration()) :
keplerianAcceleration;
return new TimeStampedFieldPVCoordinates<>(getDate(), partialPV.getPosition(), partialPV.getVelocity(), acceleration);
}
/** {@inheritDoc} */
public FieldEquinoctialOrbit<T> shiftedBy(final double dt) {
return shiftedBy(getDate().getField().getZero().add(dt));
}
/** {@inheritDoc} */
public FieldEquinoctialOrbit<T> shiftedBy(final T dt) {
// use Keplerian-only motion
final FieldEquinoctialOrbit<T> keplerianShifted = new FieldEquinoctialOrbit<>(a, ex, ey, hx, hy,
getLM().add(getKeplerianMeanMotion().multiply(dt)),
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().negate()),
keplerianShifted.partialPV.getPosition(),
one, nonKeplerianAcceleration);
// build a new orbit, taking non-Keplerian acceleration into account
return new FieldEquinoctialOrbit<>(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 equinoctial 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 FieldEquinoctialOrbit<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 previousLm = zero.add(Double.NaN);
for (final FieldOrbit<T> orbit : list) {
final FieldEquinoctialOrbit<T> equi = (FieldEquinoctialOrbit<T>) OrbitType.EQUINOCTIAL.convertType(orbit);
final T continuousLm;
if (previousDate == null) {
continuousLm = (T) equi.getLM();
} else {
final T dt = (T) equi.getDate().durationFrom(previousDate);
final T keplerLm = previousLm.add((T) equi.getKeplerianMeanMotion().multiply(dt));
continuousLm = MathUtils.normalizeAngle((T) equi.getLM(), keplerLm);
}
previousDate = equi.getDate();
previousLm = continuousLm;
final T[] toAdd = MathArrays.buildArray(field, 6);
toAdd[0] = (T) equi.getA();
toAdd[1] = (T) equi.getEquinoctialEx();
toAdd[2] = (T) equi.getEquinoctialEy();
toAdd[3] = (T) equi.getHx();
toAdd[4] = (T) equi.getHy();
toAdd[5] = (T) continuousLm;
if (useDerivatives) {
final T[] toAddDot = MathArrays.buildArray(one.getField(), 6);
toAddDot[0] = equi.getADot();
toAddDot[1] = equi.getEquinoctialExDot();
toAddDot[2] = equi.getEquinoctialEyDot();
toAddDot[3] = equi.getHxDot();
toAddDot[4] = equi.getHyDot();
toAddDot[5] = equi.getLMDot();
interpolator.addSamplePoint(equi.getDate().durationFrom(date),
toAdd, toAddDot);
} else {
interpolator.addSamplePoint((T) equi.getDate().durationFrom(date),
toAdd);
}
}
// interpolate
final T[][] interpolated = interpolator.derivatives(zero, 1);
// build a new interpolated instance
return new FieldEquinoctialOrbit<>(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() {
final T[][] jacobian = MathArrays.buildArray(field, 6, 6);
// compute various intermediate parameters
computePVWithoutA();
final FieldVector3D<T> position = partialPV.getPosition();
final FieldVector3D<T> velocity = partialPV.getVelocity();
final T r2 = position.getNormSq();
final T r = r2.sqrt();
final T r3 = r.multiply(r2);
final T mu = getMu();
final T sqrtMuA = a.multiply(mu).sqrt();
final T a2 = a.multiply(a);
final T e2 = ex.multiply(ex).add(ey.multiply(ey));
final T oMe2 = one.subtract(e2);
final T epsilon = oMe2.sqrt();
final T beta = one.divide(epsilon.add(1));
final T ratio = epsilon.multiply(beta);
final T hx2 = hx.multiply(hx);
final T hy2 = hy.multiply(hy);
final T hxhy = hx.multiply(hy);
// precomputing equinoctial frame unit vectors (f, g, w)
final FieldVector3D<T> f = new FieldVector3D<>(hx2.subtract(hy2).add(1), hxhy.multiply(2), hy.multiply(-2)).normalize();
final FieldVector3D<T> g = new FieldVector3D<>(hxhy.multiply(2), hy2.add(1).subtract(hx2), hx.multiply(2)).normalize();
final FieldVector3D<T> w = FieldVector3D.crossProduct(position, velocity).normalize();
// coordinates of the spacecraft in the equinoctial frame
final T x = FieldVector3D.dotProduct(position, f);
final T y = FieldVector3D.dotProduct(position, g);
final T xDot = FieldVector3D.dotProduct(velocity, f);
final T yDot = FieldVector3D.dotProduct(velocity, g);
// drDot / dEx = dXDot / dEx * f + dYDot / dEx * g
final T c1 = a.divide(sqrtMuA.multiply(epsilon));
final T c1N = c1.negate();
final T c2 = a.multiply(sqrtMuA).multiply(beta).divide(r3);
final T c3 = sqrtMuA.divide(r3.multiply(epsilon));
final FieldVector3D<T> drDotSdEx = new FieldVector3D<>(c1.multiply(xDot).multiply(yDot).subtract(c2.multiply(ey).multiply(x)).subtract(c3.multiply(x).multiply(y)), f,
c1N.multiply(xDot).multiply(xDot).subtract(c2.multiply(ey).multiply(y)).add(c3.multiply(x).multiply(x)), g);
// drDot / dEy = dXDot / dEy * f + dYDot / dEy * g
final FieldVector3D<T> drDotSdEy = new FieldVector3D<>(c1.multiply(yDot).multiply(yDot).add(c2.multiply(ex).multiply(x)).subtract(c3.multiply(y).multiply(y)), f,
c1N.multiply(xDot).multiply(yDot).add(c2.multiply(ex).multiply(y)).add(c3.multiply(x).multiply(y)), g);
// da
final FieldVector3D<T> vectorAR = new FieldVector3D<>(a2.multiply(2).divide(r3), position);
final FieldVector3D<T> vectorARDot = new FieldVector3D<>(a2.multiply(2).divide(mu), velocity);
fillHalfRow(one, vectorAR, jacobian[0], 0);
fillHalfRow(one, vectorARDot, jacobian[0], 3);
// dEx
final T d1 = a.negate().multiply(ratio).divide(r3);
final T d2 = (hy.multiply(xDot).subtract(hx.multiply(yDot))).divide(sqrtMuA.multiply(epsilon));
final T d3 = hx.multiply(y).subtract(hy.multiply(x)).divide(sqrtMuA);
final FieldVector3D<T> vectorExRDot =
new FieldVector3D<>(x.multiply(2).multiply(yDot).subtract(xDot.multiply(y)).divide(mu), g, y.negate().multiply(yDot).divide(mu), f, ey.negate().multiply(d3).divide(epsilon), w);
fillHalfRow(ex.multiply(d1), position, ey.negate().multiply(d2), w, epsilon.divide(sqrtMuA), drDotSdEy, jacobian[1], 0);
fillHalfRow(one, vectorExRDot, jacobian[1], 3);
// dEy
final FieldVector3D<T> vectorEyRDot =
new FieldVector3D<>(xDot.multiply(2).multiply(y).subtract(x.multiply(yDot)).divide(mu), f, x.negate().multiply(xDot).divide(mu), g, ex.multiply(d3).divide(epsilon), w);
fillHalfRow(ey.multiply(d1), position, ex.multiply(d2), w, epsilon.negate().divide(sqrtMuA), drDotSdEx, jacobian[2], 0);
fillHalfRow(one, vectorEyRDot, jacobian[2], 3);
// dHx
final T h = (hx2.add(1).add(hy2)).divide(sqrtMuA.multiply(2).multiply(epsilon));
fillHalfRow( h.negate().multiply(xDot), w, jacobian[3], 0);
fillHalfRow( h.multiply(x), w, jacobian[3], 3);
// dHy
fillHalfRow( h.negate().multiply(yDot), w, jacobian[4], 0);
fillHalfRow( h.multiply(y), w, jacobian[4], 3);
// dLambdaM
final T l = ratio.negate().divide(sqrtMuA);
fillHalfRow(one.negate().divide(sqrtMuA), velocity, d2, w, l.multiply(ex), drDotSdEx, l.multiply(ey), drDotSdEy, jacobian[5], 0);
fillHalfRow(zero.add(-2).divide(sqrtMuA), position, ex.multiply(beta), vectorEyRDot, ey.negate().multiply(beta), vectorExRDot, d3, w, jacobian[5], 3);
return jacobian;
}
/** {@inheritDoc} */
protected T[][] computeJacobianEccentricWrtCartesian() {
// start by computing the Jacobian with mean angle
final T[][] jacobian = computeJacobianMeanWrtCartesian();
// Differentiating the Kepler equation lM = lE - ex sin lE + ey cos lE leads to:
// dlM = (1 - ex cos lE - ey sin lE) dE - sin lE dex + cos lE dey
// which is inverted and rewritten as:
// dlE = a/r dlM + sin lE a/r dex - cos lE a/r dey
final FieldSinCos<T> scLe = FastMath.sinCos(getLE());
final T cosLe = scLe.cos();
final T sinLe = scLe.sin();
final T aOr = one.divide(one.subtract(ex.multiply(cosLe)).subtract(ey.multiply(sinLe)));
// update longitude row
final T[] rowEx = jacobian[1];
final T[] rowEy = jacobian[2];
final T[] rowL = jacobian[5];
for (int j = 0; j < 6; ++j) {
rowL[j] = aOr.multiply(rowL[j].add(sinLe.multiply(rowEx[j])).subtract(cosLe.multiply(rowEy[j])));
}
return jacobian;
}
/** {@inheritDoc} */
protected T[][] computeJacobianTrueWrtCartesian() {
// start by computing the Jacobian with eccentric angle
final T[][] jacobian = computeJacobianEccentricWrtCartesian();
// Differentiating the eccentric longitude equation
// tan((lV - lE)/2) = [ex sin lE - ey cos lE] / [sqrt(1-ex^2-ey^2) + 1 - ex cos lE - ey sin lE]
// leads to
// cT (dlV - dlE) = cE dlE + cX dex + cY dey
// with
// cT = [d^2 + (ex sin lE - ey cos lE)^2] / 2
// d = 1 + sqrt(1-ex^2-ey^2) - ex cos lE - ey sin lE
// cE = (ex cos lE + ey sin lE) (sqrt(1-ex^2-ey^2) + 1) - ex^2 - ey^2
// cX = sin lE (sqrt(1-ex^2-ey^2) + 1) - ey + ex (ex sin lE - ey cos lE) / sqrt(1-ex^2-ey^2)
// cY = -cos lE (sqrt(1-ex^2-ey^2) + 1) + ex + ey (ex sin lE - ey cos lE) / sqrt(1-ex^2-ey^2)
// which can be solved to find the differential of the true longitude
// dlV = (cT + cE) / cT dlE + cX / cT deX + cY / cT deX
final FieldSinCos<T> scLe = FastMath.sinCos(getLE());
final T cosLe = scLe.cos();
final T sinLe = scLe.sin();
final T eSinE = ex.multiply(sinLe).subtract(ey.multiply(cosLe));
final T ecosE = ex.multiply(cosLe).add(ey.multiply(sinLe));
final T e2 = ex.multiply(ex).add(ey.multiply(ey));
final T epsilon = one.subtract(e2).sqrt();
final T onePeps = epsilon.add(1);
final T d = onePeps.subtract(ecosE);
final T cT = d.multiply(d).add(eSinE.multiply(eSinE)).divide(2);
final T cE = ecosE.multiply(onePeps).subtract(e2);
final T cX = ex.multiply(eSinE).divide(epsilon).subtract(ey).add(sinLe.multiply(onePeps));
final T cY = ey.multiply(eSinE).divide(epsilon).add( ex).subtract(cosLe.multiply(onePeps));
final T factorLe = cT.add(cE).divide(cT);
final T factorEx = cX.divide(cT);
final T factorEy = cY.divide(cT);
// update longitude row
final T[] rowEx = jacobian[1];
final T[] rowEy = jacobian[2];
final T[] rowL = jacobian[5];
for (int j = 0; j < 6; ++j) {
rowL[j] = factorLe.multiply(rowL[j]).add(factorEx.multiply(rowEx[j])).add(factorEy.multiply(rowEy[j]));
}
return jacobian;
}
/** {@inheritDoc} */
public void addKeplerContribution(final PositionAngle type, final T gm,
final T[] pDot) {
final T oMe2;
final T ksi;
final T n = gm.divide(a).sqrt().divide(a);
final FieldSinCos<T> sc = FastMath.sinCos(lv);
switch (type) {
case MEAN :
pDot[5] = pDot[5].add(n);
break;
case ECCENTRIC :
oMe2 = one.subtract(ex.multiply(ex)).subtract(ey.multiply(ey));
ksi = ex.multiply(sc.cos()).add(1).add(ey.multiply(sc.sin()));
pDot[5] = pDot[5].add(n.multiply(ksi).divide(oMe2));
break;
case TRUE :
oMe2 = one.subtract(ex.multiply(ex)).subtract(ey.multiply(ey));
ksi = ex.multiply(sc.cos()).add(1).add(ey.multiply(sc.sin()));
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 equinoctial parameters object.
* @return a string representation of this object
*/
public String toString() {
return new StringBuilder().append("equinoctial parameters: ").append('{').
append("a: ").append(a.getReal()).
append("; ex: ").append(ex.getReal()).append("; ey: ").append(ey.getReal()).
append("; hx: ").append(hx.getReal()).append("; hy: ").append(hy.getReal()).
append("; lv: ").append(FastMath.toDegrees(lv.getReal())).
append(";}").toString();
}
/** {@inheritDoc} */
@Override
public EquinoctialOrbit toOrbit() {
if (hasDerivatives()) {
return new EquinoctialOrbit(a.getReal(), ex.getReal(), ey.getReal(),
hx.getReal(), hy.getReal(), lv.getReal(),
aDot.getReal(), exDot.getReal(), eyDot.getReal(),
hxDot.getReal(), hyDot.getReal(), lvDot.getReal(),
PositionAngle.TRUE, getFrame(),
getDate().toAbsoluteDate(), getMu().getReal());
} else {
return new EquinoctialOrbit(a.getReal(), ex.getReal(), ey.getReal(),
hx.getReal(), hy.getReal(), lv.getReal(),
PositionAngle.TRUE, getFrame(),
getDate().toAbsoluteDate(), getMu().getReal());
}
}
}