FieldCircularOrbit.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.List;
import java.util.stream.Collectors;
import java.util.stream.Stream;
import org.hipparchus.RealFieldElement;
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.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 circular orbital parameters.
* <p>
* The parameters used internally are the circular elements which can be
* related to Keplerian elements as follows:
* <ul>
* <li>a</li>
* <li>e<sub>x</sub> = e cos(ω)</li>
* <li>e<sub>y</sub> = e sin(ω)</li>
* <li>i</li>
* <li>Ω</li>
* <li>α<sub>v</sub> = v + ω</li>
* </ul>
* where Ω stands for the Right Ascension of the Ascending Node and
* α<sub>v</sub> stands for the true latitude argument
* <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 circular (but not equatorial), the circular
* parameters are still unambiguously defined whereas some Keplerian elements
* (more precisely ω and Ω) become ambiguous. When orbit is equatorial,
* neither the Keplerian nor the circular parameters can be defined unambiguously.
* {@link EquinoctialOrbit equinoctial orbits} is the recommended way to represent
* orbits.
* </p>
* <p>
* The instance <code>CircularOrbit</code> is guaranteed to be immutable.
* </p>
* @see Orbit
* @see KeplerianOrbit
* @see CartesianOrbit
* @see EquinoctialOrbit
* @author Luc Maisonobe
* @author Fabien Maussion
* @author Véronique Pommier-Maurussane
* @since 9.0
*/
public class FieldCircularOrbit<T extends RealFieldElement<T>>
extends FieldOrbit<T> {
/** Semi-major axis (m). */
private final T a;
/** First component of the circular eccentricity vector. */
private final T ex;
/** Second component of the circular eccentricity vector. */
private final T ey;
/** Inclination (rad). */
private final T i;
/** Right Ascension of Ascending Node (rad). */
private final T raan;
/** True latitude argument (rad). */
private final T alphaV;
/** Semi-major axis derivative (m/s). */
private final T aDot;
/** First component of the circular eccentricity vector derivative. */
private final T exDot;
/** Second component of the circular eccentricity vector derivative. */
private final T eyDot;
/** Inclination derivative (rad/s). */
private final T iDot;
/** Right Ascension of Ascending Node derivative (rad/s). */
private final T raanDot;
/** True latitude argument derivative (rad/s). */
private final T alphaVDot;
/** Partial Cartesian coordinates (position and velocity are valid, acceleration may be missing). */
private FieldPVCoordinates<T> partialPV;
/** one. */
private final T one;
/** zero. */
private final T zero;
/** Creates a new instance.
* @param a semi-major axis (m)
* @param ex e cos(ω), first component of circular eccentricity vector
* @param ey e sin(ω), second component of circular eccentricity vector
* @param i inclination (rad)
* @param raan right ascension of ascending node (Ω, rad)
* @param alpha an + ω, mean, eccentric or true latitude argument (rad)
* @param type type of latitude argument
* @param frame the frame in which are defined the parameters
* (<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 FieldCircularOrbit(final T a, final T ex, final T ey,
final T i, final T raan,
final T alpha, final PositionAngle type,
final Frame frame, final FieldAbsoluteDate<T> date, final T mu)
throws IllegalArgumentException {
this(a, ex, ey, i, raan, alpha,
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), first component of circular eccentricity vector
* @param ey e sin(ω), second component of circular eccentricity vector
* @param i inclination (rad)
* @param raan right ascension of ascending node (Ω, rad)
* @param alpha an + ω, mean, eccentric or true latitude argument (rad)
* @param aDot semi-major axis derivative (m/s)
* @param exDot d(e cos(ω))/dt, first component of circular eccentricity vector derivative
* @param eyDot d(e sin(ω))/dt, second component of circular eccentricity vector derivative
* @param iDot inclination derivative(rad/s)
* @param raanDot right ascension of ascending node derivative (rad/s)
* @param alphaDot d(an + ω), mean, eccentric or true latitude argument derivative (rad/s)
* @param type type of latitude argument
* @param frame the frame in which are defined the parameters
* (<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 FieldCircularOrbit(final T a, final T ex, final T ey,
final T i, final T raan, final T alpha,
final T aDot, final T exDot, final T eyDot,
final T iDot, final T raanDot, final T alphaDot,
final PositionAngle type,
final Frame frame, final FieldAbsoluteDate<T> date, final T mu)
throws IllegalArgumentException {
super(frame, date, mu);
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.i = i;
this.iDot = iDot;
this.raan = raan;
this.raanDot = raanDot;
one = a.getField().getOne();
zero = a.getField().getZero();
if (hasDerivatives()) {
final FieldUnivariateDerivative1<T> exUD = new FieldUnivariateDerivative1<>(ex, exDot);
final FieldUnivariateDerivative1<T> eyUD = new FieldUnivariateDerivative1<>(ey, eyDot);
final FieldUnivariateDerivative1<T> alphaUD = new FieldUnivariateDerivative1<>(alpha, alphaDot);
final FieldUnivariateDerivative1<T> alphavUD;
switch (type) {
case MEAN :
alphavUD = eccentricToTrue(meanToEccentric(alphaUD, exUD, eyUD), exUD, eyUD);
break;
case ECCENTRIC :
alphavUD = eccentricToTrue(alphaUD, exUD, eyUD);
break;
case TRUE :
alphavUD = alphaUD;
break;
default :
throw new OrekitInternalError(null);
}
this.alphaV = alphavUD.getValue();
this.alphaVDot = alphavUD.getDerivative(1);
} else {
switch (type) {
case MEAN :
this.alphaV = eccentricToTrue(meanToEccentric(alpha, ex, ey), ex, ey);
break;
case ECCENTRIC :
this.alphaV = eccentricToTrue(alpha, ex, ey);
break;
case TRUE :
this.alphaV = alpha;
break;
default :
throw new OrekitInternalError(null);
}
this.alphaVDot = null;
}
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 {@link FieldPVCoordinates} in inertial frame
* @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 FieldCircularOrbit(final TimeStampedFieldPVCoordinates<T> pvCoordinates,
final Frame frame, final T mu)
throws IllegalArgumentException {
super(pvCoordinates, frame, mu);
// 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);
zero = r.getField().getZero();
one = r.getField().getOne();
if (rV2OnMu.getReal() > 2) {
throw new OrekitIllegalArgumentException(OrekitMessages.HYPERBOLIC_ORBIT_NOT_HANDLED_AS,
getClass().getName());
}
a = r.divide(rV2OnMu.negate().add(2));
// compute inclination
final FieldVector3D<T> momentum = pvCoordinates.getMomentum();
final FieldVector3D<T> plusK = FieldVector3D.getPlusK(r.getField());
i = FieldVector3D.angle(momentum, plusK);
// compute right ascension of ascending node
final FieldVector3D<T> node = FieldVector3D.crossProduct(plusK, momentum);
raan = node.getY().atan2(node.getX());
// 2D-coordinates in the canonical frame
final T cosRaan = raan.cos();
final T sinRaan = raan.sin();
final T cosI = i.cos();
final T sinI = i.sin();
final T xP = pvP.getX();
final T yP = pvP.getY();
final T zP = pvP.getZ();
final T x2 = (xP.multiply(cosRaan).add(yP .multiply(sinRaan))).divide(a);
final T y2 = (yP.multiply(cosRaan).subtract(xP.multiply(sinRaan))).multiply(cosI).add(zP.multiply(sinI)).divide(a);
// 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 = eSE.multiply(e2.negate().add(1).sqrt());
final T aOnR = a.divide(r);
final T a2OnR2 = aOnR.multiply(aOnR);
ex = a2OnR2.multiply(f.multiply(x2).add(g.multiply(y2)));
ey = a2OnR2.multiply(f.multiply(y2).subtract(g.multiply(x2)));
// compute latitude argument
final T beta = (ex.multiply(ex).add(ey.multiply(ey)).negate().add(1)).sqrt().add(1).reciprocal();
alphaV = eccentricToTrue(y2.add(ey).add(eSE.multiply(beta).multiply(ex)).atan2(x2.add(ex).subtract(eSE.multiply(beta).multiply(ey))),
ex, ey);
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));
iDot = 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 alphaMDot = 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> alphaMUD = new FieldUnivariateDerivative1<>(getAlphaM(), alphaMDot);
final FieldUnivariateDerivative1<T> alphavUD = eccentricToTrue(meanToEccentric(alphaMUD, exUD, eyUD), exUD, eyUD);
alphaVDot = alphavUD.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;
iDot = null;
raanDot = null;
alphaVDot = 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 {@link FieldPVCoordinates} in inertial frame
* @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 FieldCircularOrbit(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 FieldCircularOrbit(final FieldOrbit<T> op) {
super(op.getFrame(), op.getDate(), op.getMu());
a = op.getA();
i = op.getI();
final T hx = op.getHx();
final T hy = op.getHy();
final T h2 = hx.multiply(hx).add(hy.multiply(hy));
final T h = h2.sqrt();
raan = hy.atan2(hx);
final T cosRaan = h.getReal() == 0 ? raan.cos() : hx.divide(h);
final T sinRaan = h.getReal() == 0 ? raan.sin() : hy.divide(h);
final T equiEx = op.getEquinoctialEx();
final T equiEy = op.getEquinoctialEy();
ex = equiEx.multiply(cosRaan).add(equiEy.multiply(sinRaan));
ey = equiEy.multiply(cosRaan).subtract(equiEx.multiply(sinRaan));
this.alphaV = op.getLv().subtract(raan);
if (op.hasDerivatives()) {
aDot = op.getADot();
final T hxDot = op.getHxDot();
final T hyDot = op.getHyDot();
iDot = cosRaan.multiply(hxDot).add(sinRaan.multiply(hyDot)).multiply(2).divide(h2.add(1));
raanDot = hx.multiply(hyDot).subtract(hy.multiply(hxDot)).divide(h2);
final T equiExDot = op.getEquinoctialExDot();
final T equiEyDot = op.getEquinoctialEyDot();
exDot = equiExDot.add(equiEy.multiply(raanDot)).multiply(cosRaan).
add(equiEyDot.subtract(equiEx.multiply(raanDot)).multiply(sinRaan));
eyDot = equiEyDot.subtract(equiEx.multiply(raanDot)).multiply(cosRaan).
subtract(equiExDot.add(equiEy.multiply(raanDot)).multiply(sinRaan));
alphaVDot = op.getLvDot().subtract(raanDot);
} else {
aDot = null;
exDot = null;
eyDot = null;
iDot = null;
raanDot = null;
alphaVDot = null;
}
partialPV = null;
one = a.getField().getOne();
zero = a.getField().getZero();
}
/** {@inheritDoc} */
public OrbitType getType() {
return OrbitType.CIRCULAR;
}
/** {@inheritDoc} */
public T getA() {
return a;
}
/** {@inheritDoc} */
public T getADot() {
return aDot;
}
/** {@inheritDoc} */
public T getEquinoctialEx() {
return ex.multiply(raan.cos()).subtract(ey.multiply(raan.sin()));
}
/** {@inheritDoc} */
public T getEquinoctialExDot() {
if (!hasDerivatives()) {
return null;
}
final T cosRaan = raan.cos();
final T sinRaan = raan.sin();
return exDot.subtract(ey.multiply(raanDot)).multiply(cosRaan).
subtract(eyDot.add(ex.multiply(raanDot)).multiply(sinRaan));
}
/** {@inheritDoc} */
public T getEquinoctialEy() {
return ey.multiply(raan.cos()).add(ex.multiply(raan.sin()));
}
/** {@inheritDoc} */
public T getEquinoctialEyDot() {
if (!hasDerivatives()) {
return null;
}
final T cosRaan = raan.cos();
final T sinRaan = raan.sin();
return eyDot.add(ex.multiply(raanDot)).multiply(cosRaan).
add(exDot.subtract(ey.multiply(raanDot)).multiply(sinRaan));
}
/** Get the first component of the circular eccentricity vector.
* @return ex = e cos(ω), first component of the circular eccentricity vector
*/
public T getCircularEx() {
return ex;
}
/** Get the first component of the circular eccentricity vector derivative.
* @return d(ex)/dt = d(e cos(ω))/dt, first component of the circular eccentricity vector derivative
*/
public T getCircularExDot() {
return exDot;
}
/** Get the second component of the circular eccentricity vector.
* @return ey = e sin(ω), second component of the circular eccentricity vector
*/
public T getCircularEy() {
return ey;
}
/** Get the second component of the circular eccentricity vector derivative.
* @return d(ey)/dt = d(e sin(ω))/dt, second component of the circular eccentricity vector derivative
*/
public T getCircularEyDot() {
return eyDot;
}
/** {@inheritDoc} */
public T getHx() {
// Check for equatorial retrograde orbit
if (FastMath.abs(i.getReal() - FastMath.PI) < 1.0e-10) {
return 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 zero.add(Double.NaN);
}
final T cosRaan = raan.cos();
final T sinRaan = raan.sin();
final T tan = i.multiply(0.5).tan();
return cosRaan.multiply(0.5).multiply(tan.multiply(tan).add(1)).multiply(iDot).
subtract(sinRaan.multiply(tan).multiply(raanDot));
}
/** {@inheritDoc} */
public T getHy() {
// Check for equatorial retrograde orbit
if (FastMath.abs(i.getReal() - FastMath.PI) < 1.0e-10) {
return 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 zero.add(Double.NaN);
}
final T cosRaan = raan.cos();
final T sinRaan = raan.sin();
final T tan = i.multiply(0.5).tan();
return sinRaan.multiply(0.5).multiply(tan.multiply(tan).add(1)).multiply(iDot).
add(cosRaan.multiply(tan).multiply(raanDot));
}
/** Get the true latitude argument.
* @return v + ω true latitude argument (rad)
*/
public T getAlphaV() {
return alphaV;
}
/** Get the true latitude argument derivative.
* @return d(v + ω)/dt true latitude argument derivative (rad/s)
*/
public T getAlphaVDot() {
return alphaVDot;
}
/** Get the eccentric latitude argument.
* @return E + ω eccentric latitude argument (rad)
*/
public T getAlphaE() {
return trueToEccentric(alphaV, ex, ey);
}
/** Get the eccentric latitude argument derivative.
* @return d(E + ω)/dt eccentric latitude argument derivative (rad/s)
*/
public T getAlphaEDot() {
if (!hasDerivatives()) {
return null;
}
final FieldUnivariateDerivative1<T> alphaVUD = new FieldUnivariateDerivative1<>(alphaV, alphaVDot);
final FieldUnivariateDerivative1<T> exUD = new FieldUnivariateDerivative1<>(ex, exDot);
final FieldUnivariateDerivative1<T> eyUD = new FieldUnivariateDerivative1<>(ey, eyDot);
final FieldUnivariateDerivative1<T> alphaEUD = trueToEccentric(alphaVUD, exUD, eyUD);
return alphaEUD.getDerivative(1);
}
/** Get the mean latitude argument.
* @return M + ω mean latitude argument (rad)
*/
public T getAlphaM() {
return eccentricToMean(trueToEccentric(alphaV, ex, ey), ex, ey);
}
/** Get the mean latitude argument derivative.
* @return d(M + ω)/dt mean latitude argument derivative (rad/s)
*/
public T getAlphaMDot() {
if (!hasDerivatives()) {
return null;
}
final FieldUnivariateDerivative1<T> alphaVUD = new FieldUnivariateDerivative1<>(alphaV, alphaVDot);
final FieldUnivariateDerivative1<T> exUD = new FieldUnivariateDerivative1<>(ex, exDot);
final FieldUnivariateDerivative1<T> eyUD = new FieldUnivariateDerivative1<>(ey, eyDot);
final FieldUnivariateDerivative1<T> alphaMUD = eccentricToMean(trueToEccentric(alphaVUD, exUD, eyUD), exUD, eyUD);
return alphaMUD.getDerivative(1);
}
/** Get the latitude argument.
* @param type type of the angle
* @return latitude argument (rad)
*/
public T getAlpha(final PositionAngle type) {
return (type == PositionAngle.MEAN) ? getAlphaM() :
((type == PositionAngle.ECCENTRIC) ? getAlphaE() :
getAlphaV());
}
/** Get the latitude argument derivative.
* @param type type of the angle
* @return latitude argument derivative (rad/s)
*/
public T getAlphaDot(final PositionAngle type) {
return (type == PositionAngle.MEAN) ? getAlphaMDot() :
((type == PositionAngle.ECCENTRIC) ? getAlphaEDot() :
getAlphaVDot());
}
/** Computes the true latitude argument from the eccentric latitude argument.
* @param alphaE = E + ω eccentric latitude argument (rad)
* @param ex e cos(ω), first component of circular eccentricity vector
* @param ey e sin(ω), second component of circular eccentricity vector
* @param <T> Type of the field elements
* @return the true latitude argument.
*/
public static <T extends RealFieldElement<T>> T eccentricToTrue(final T alphaE, final T ex, final T ey) {
final T epsilon = ex.multiply(ex).add(ey.multiply(ey)).negate().add(1).sqrt();
final T cosAlphaE = alphaE.cos();
final T sinAlphaE = alphaE.sin();
return alphaE.add(ex.multiply(sinAlphaE).subtract(ey.multiply(cosAlphaE)).divide(
epsilon.add(1).subtract(ex.multiply(cosAlphaE)).subtract(
ey.multiply(sinAlphaE))).atan().multiply(2));
}
/** Computes the eccentric latitude argument from the true latitude argument.
* @param alphaV = v + ω true latitude argument (rad)
* @param ex e cos(ω), first component of circular eccentricity vector
* @param ey e sin(ω), second component of circular eccentricity vector
* @param <T> Type of the field elements
* @return the eccentric latitude argument.
*/
public static <T extends RealFieldElement<T>> T trueToEccentric(final T alphaV, final T ex, final T ey) {
final T epsilon = ex.multiply(ex).add(ey.multiply(ey)).negate().add(1).sqrt();
final T cosAlphaV = alphaV.cos();
final T sinAlphaV = alphaV.sin();
return alphaV.add(ey.multiply(cosAlphaV).subtract(ex.multiply(sinAlphaV)).divide
(epsilon.add(1).add(ex.multiply(cosAlphaV).add(ey.multiply(sinAlphaV)))).atan().multiply(2));
}
/** Computes the eccentric latitude argument from the mean latitude argument.
* @param alphaM = M + ω mean latitude argument (rad)
* @param ex e cos(ω), first component of circular eccentricity vector
* @param ey e sin(ω), second component of circular eccentricity vector
* @param <T> Type of the field elements
* @return the eccentric latitude argument.
*/
public static <T extends RealFieldElement<T>> T meanToEccentric(final T alphaM, final T ex, final T ey) {
// Generalization of Kepler equation to circular parameters
// with alphaE = PA + E and
// alphaM = PA + M = alphaE - ex.sin(alphaE) + ey.cos(alphaE)
T alphaE = alphaM;
T shift = alphaM.getField().getZero();
T alphaEMalphaM = alphaM.getField().getZero();
T cosAlphaE = alphaE.cos();
T sinAlphaE = alphaE.sin();
int iter = 0;
do {
final T f2 = ex.multiply(sinAlphaE).subtract(ey.multiply(cosAlphaE));
final T f1 = ex.negate().multiply(cosAlphaE).subtract(ey.multiply(sinAlphaE)).add(1);
final T f0 = alphaEMalphaM.subtract(f2);
final T f12 = f1.multiply(2);
shift = f0.multiply(f12).divide(f1.multiply(f12).subtract(f0.multiply(f2)));
alphaEMalphaM = alphaEMalphaM.subtract(shift);
alphaE = alphaM.add(alphaEMalphaM);
cosAlphaE = alphaE.cos();
sinAlphaE = alphaE.sin();
} while ((++iter < 50) && (FastMath.abs(shift.getReal()) > 1.0e-12));
return alphaE;
}
/** Computes the mean latitude argument from the eccentric latitude argument.
* @param alphaE = E + ω eccentric latitude argument (rad)
* @param ex e cos(ω), first component of circular eccentricity vector
* @param ey e sin(ω), second component of circular eccentricity vector
* @param <T> Type of the field elements
* @return the mean latitude argument.
*/
public static <T extends RealFieldElement<T>> T eccentricToMean(final T alphaE, final T ex, final T ey) {
return alphaE.subtract(ex.multiply(alphaE.sin()).subtract(ey.multiply(alphaE.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(getE());
}
/** {@inheritDoc} */
public T getI() {
return i;
}
/** {@inheritDoc} */
public T getIDot() {
return iDot;
}
/** 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.
* @return right ascension of the ascending node derivative (rad/s)
*/
public T getRightAscensionOfAscendingNodeDot() {
return raanDot;
}
/** {@inheritDoc} */
public T getLv() {
return alphaV.add(raan);
}
/** {@inheritDoc} */
public T getLvDot() {
return hasDerivatives() ? alphaVDot.add(raanDot) : null;
}
/** {@inheritDoc} */
public T getLE() {
return getAlphaE().add(raan);
}
/** {@inheritDoc} */
public T getLEDot() {
return hasDerivatives() ? getAlphaEDot().add(raanDot) : null;
}
/** {@inheritDoc} */
public T getLM() {
return getAlphaM().add(raan);
}
/** {@inheritDoc} */
public T getLMDot() {
return hasDerivatives() ? getAlphaMDot().add(raanDot) : null;
}
/** {@inheritDoc} */
@Override
public boolean hasDerivatives() {
return aDot != null;
}
/** Compute position and velocity but not acceleration.
*/
private void computePVWithoutA() {
if (partialPV != null) {
// already computed
return;
}
// get equinoctial parameters
final T equEx = getEquinoctialEx();
final T equEy = getEquinoctialEy();
final T hx = getHx();
final T hy = getHy();
final T lE = getLE();
// inclination-related intermediate parameters
final T hx2 = hx.multiply(hx);
final T hy2 = hy.multiply(hy);
final T factH = (hx2.add(1).add(hy2)).reciprocal();
// reference axes defining the orbital plane
final T ux = (hx2.add(1).subtract(hy2)).multiply(factH);
final T uy = hx.multiply(2).multiply(hy).multiply(factH);
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 exey = equEx.multiply(equEy);
final T ex2 = equEx.multiply(equEx);
final T ey2 = equEy.multiply(equEy);
final T e2 = ex2.add(ey2);
final T eta = e2.negate().add(1).sqrt().add(1);
final T beta = eta.reciprocal();
// eccentric latitude argument
final T cLe = lE.cos();
final T sLe = lE.sin();
final T exCeyS = equEx.multiply(cLe).add(equEy.multiply(sLe));
// coordinates of position and velocity in the orbital plane
final T x = a.multiply(beta.negate().multiply(ey2).add(1).multiply(cLe).add(beta.multiply(exey).multiply(sLe)).subtract(equEx));
final T y = a.multiply(beta.negate().multiply(ex2).add(1).multiply(sLe).add(beta.multiply(exey).multiply(cLe)).subtract(equEy));
final T factor = one.add(getMu()).divide(a).sqrt().divide(exCeyS.negate().add(1));
final T xdot = factor.multiply( beta.multiply(equEy).multiply(exCeyS).subtract(sLe ));
final T ydot = factor.multiply( cLe.subtract(beta.multiply(equEx).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 = getAlphaMDot().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(iDot)).
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(exDot)).
add(dCdP[4][2].multiply(eyDot)).
add(dCdP[4][3].multiply(iDot)).
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(exDot)).
add(dCdP[5][2].multiply(eyDot)).
add(dCdP[5][3].multiply(iDot)).
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().negate()),
partialPV.getPosition());
final FieldVector3D<T> acceleration = hasDerivatives() ?
keplerianAcceleration.add(nonKeplerianAcceleration()) :
keplerianAcceleration;
return new TimeStampedFieldPVCoordinates<>(getDate(), partialPV.getPosition(), partialPV.getVelocity(), acceleration);
}
/** {@inheritDoc} */
public FieldCircularOrbit<T> shiftedBy(final double dt) {
return shiftedBy(getDate().getField().getZero().add(dt));
}
/** {@inheritDoc} */
public FieldCircularOrbit<T> shiftedBy(final T dt) {
// use Keplerian-only motion
final FieldCircularOrbit<T> keplerianShifted = new FieldCircularOrbit<>(a, ex, ey, i, raan,
getAlphaM().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 FieldCircularOrbit<>(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 circular 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 FieldCircularOrbit<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 previousRAAN = zero.add(Double.NaN);
T previousAlphaM = zero.add(Double.NaN);
for (final FieldOrbit<T> orbit : list) {
final FieldCircularOrbit<T> circ = (FieldCircularOrbit<T>) OrbitType.CIRCULAR.convertType(orbit);
final T continuousRAAN;
final T continuousAlphaM;
if (previousDate == null) {
continuousRAAN = circ.getRightAscensionOfAscendingNode();
continuousAlphaM = circ.getAlphaM();
} else {
final T dt = circ.getDate().durationFrom(previousDate);
final T keplerAM = previousAlphaM .add(circ.getKeplerianMeanMotion().multiply(dt));
continuousRAAN = MathUtils.normalizeAngle(circ.getRightAscensionOfAscendingNode(), previousRAAN);
continuousAlphaM = MathUtils.normalizeAngle(circ.getAlphaM(), keplerAM);
}
previousDate = circ.getDate();
previousRAAN = continuousRAAN;
previousAlphaM = continuousAlphaM;
final T[] toAdd = MathArrays.buildArray(one.getField(), 6);
toAdd[0] = circ.getA();
toAdd[1] = circ.getCircularEx();
toAdd[2] = circ.getCircularEy();
toAdd[3] = circ.getI();
toAdd[4] = continuousRAAN;
toAdd[5] = continuousAlphaM;
if (useDerivatives) {
final T[] toAddDot = MathArrays.buildArray(one.getField(), 6);
toAddDot[0] = circ.getADot();
toAddDot[1] = circ.getCircularExDot();
toAddDot[2] = circ.getCircularEyDot();
toAddDot[3] = circ.getIDot();
toAddDot[4] = circ.getRightAscensionOfAscendingNodeDot();
toAddDot[5] = circ.getAlphaMDot();
interpolator.addSamplePoint(circ.getDate().durationFrom(date),
toAdd, toAddDot);
} else {
interpolator.addSamplePoint(circ.getDate().durationFrom(date),
toAdd);
}
}
// interpolate
final T[][] interpolated = interpolator.derivatives(zero, 1);
// build a new interpolated instance
return new FieldCircularOrbit<>(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(one.getField(), 6, 6);
// compute various intermediate parameters
computePVWithoutA();
final FieldVector3D<T> position = partialPV.getPosition();
final FieldVector3D<T> velocity = partialPV.getVelocity();
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 pv = FieldVector3D.dotProduct(position, velocity);
final T r2 = position.getNormSq();
final T r = r2.sqrt();
final T v2 = velocity.getNormSq();
final T mu = getMu();
final T oOsqrtMuA = one.divide(a.multiply(mu).sqrt());
final T rOa = r.divide(a);
final T aOr = a.divide(r);
final T aOr2 = a.divide(r2);
final T a2 = a.multiply(a);
final T ex2 = ex.multiply(ex);
final T ey2 = ey.multiply(ey);
final T e2 = ex2.add(ey2);
final T epsilon = e2.negate().add(1.0).sqrt();
final T beta = epsilon.add(1).reciprocal();
final T eCosE = rOa.negate().add(1);
final T eSinE = pv.multiply(oOsqrtMuA);
final T cosI = i.cos();
final T sinI = i.sin();
final T cosRaan = raan.cos();
final T sinRaan = raan.sin();
// da
fillHalfRow(aOr.multiply(2.0).multiply(aOr2), position, jacobian[0], 0);
fillHalfRow(a2.multiply(mu.divide(2.).reciprocal()), velocity, jacobian[0], 3);
// differentials of the normalized momentum
final FieldVector3D<T> danP = new FieldVector3D<>(v2, position, pv.negate(), velocity);
final FieldVector3D<T> danV = new FieldVector3D<>(r2, velocity, pv.negate(), position);
final T recip = partialPV.getMomentum().getNorm().reciprocal();
final T recip2 = recip.multiply(recip);
final T recip2N = recip2.negate();
final FieldVector3D<T> dwXP = new FieldVector3D<>(recip,
new FieldVector3D<>(zero, vz, vy.negate()),
recip2N.multiply(sinRaan).multiply(sinI),
danP);
final FieldVector3D<T> dwYP = new FieldVector3D<>(recip,
new FieldVector3D<>(vz.negate(), zero, vx),
recip2.multiply(cosRaan).multiply(sinI),
danP);
final FieldVector3D<T> dwZP = new FieldVector3D<>(recip,
new FieldVector3D<>(vy, vx.negate(), zero),
recip2N.multiply(cosI),
danP);
final FieldVector3D<T> dwXV = new FieldVector3D<>(recip,
new FieldVector3D<>(zero, z.negate(), y),
recip2N.multiply(sinRaan).multiply(sinI),
danV);
final FieldVector3D<T> dwYV = new FieldVector3D<>(recip,
new FieldVector3D<>(z, zero, x.negate()),
recip2.multiply(cosRaan).multiply(sinI),
danV);
final FieldVector3D<T> dwZV = new FieldVector3D<>(recip,
new FieldVector3D<>(y.negate(), x, zero),
recip2N.multiply(cosI),
danV);
// di
fillHalfRow(sinRaan.multiply(cosI), dwXP, cosRaan.negate().multiply(cosI), dwYP, sinI.negate(), dwZP, jacobian[3], 0);
fillHalfRow(sinRaan.multiply(cosI), dwXV, cosRaan.negate().multiply(cosI), dwYV, sinI.negate(), dwZV, jacobian[3], 3);
// dRaan
fillHalfRow(sinRaan.divide(sinI), dwYP, cosRaan.divide(sinI), dwXP, jacobian[4], 0);
fillHalfRow(sinRaan.divide(sinI), dwYV, cosRaan.divide(sinI), dwXV, jacobian[4], 3);
// orbital frame: (p, q, w) p along ascending node, w along momentum
// the coordinates of the spacecraft in this frame are: (u, v, 0)
final T u = x.multiply(cosRaan).add(y.multiply(sinRaan));
final T cv = x.negate().multiply(sinRaan).add(y.multiply(cosRaan));
final T v = cv.multiply(cosI).add(z.multiply(sinI));
// du
final FieldVector3D<T> duP = new FieldVector3D<>(cv.multiply(cosRaan).divide(sinI), dwXP,
cv.multiply(sinRaan).divide(sinI), dwYP,
one, new FieldVector3D<>(cosRaan, sinRaan, zero));
final FieldVector3D<T> duV = new FieldVector3D<>(cv.multiply(cosRaan).divide(sinI), dwXV,
cv.multiply(sinRaan).divide(sinI), dwYV);
// dv
final FieldVector3D<T> dvP = new FieldVector3D<>(u.negate().multiply(cosRaan).multiply(cosI).divide(sinI).add(sinRaan.multiply(z)), dwXP,
u.negate().multiply(sinRaan).multiply(cosI).divide(sinI).subtract(cosRaan.multiply(z)), dwYP,
cv, dwZP,
one, new FieldVector3D<>(sinRaan.negate().multiply(cosI), cosRaan.multiply(cosI), sinI));
final FieldVector3D<T> dvV = new FieldVector3D<>(u.negate().multiply(cosRaan).multiply(cosI).divide(sinI).add(sinRaan.multiply(z)), dwXV,
u.negate().multiply(sinRaan).multiply(cosI).divide(sinI).subtract(cosRaan.multiply(z)), dwYV,
cv, dwZV);
final FieldVector3D<T> dc1P = new FieldVector3D<>(aOr2.multiply(eSinE.multiply(eSinE).multiply(2).add(1).subtract(eCosE)).divide(r2), position,
aOr2.multiply(-2).multiply(eSinE).multiply(oOsqrtMuA), velocity);
final FieldVector3D<T> dc1V = new FieldVector3D<>(aOr2.multiply(-2).multiply(eSinE).multiply(oOsqrtMuA), position,
zero.add(2).divide(mu), velocity);
final FieldVector3D<T> dc2P = new FieldVector3D<>(aOr2.multiply(eSinE).multiply(eSinE.multiply(eSinE).subtract(e2.negate().add(1))).divide(r2.multiply(epsilon)), position,
aOr2.multiply(e2.negate().add(1).subtract(eSinE.multiply(eSinE))).multiply(oOsqrtMuA).divide(epsilon), velocity);
final FieldVector3D<T> dc2V = new FieldVector3D<>(aOr2.multiply(e2.negate().add(1).subtract(eSinE.multiply(eSinE))).multiply(oOsqrtMuA).divide(epsilon), position,
eSinE.divide(epsilon.multiply(mu)), velocity);
final T cof1 = aOr2.multiply(eCosE.subtract(e2));
final T cof2 = aOr2.multiply(epsilon).multiply(eSinE);
final FieldVector3D<T> dexP = new FieldVector3D<>(u, dc1P, v, dc2P, cof1, duP, cof2, dvP);
final FieldVector3D<T> dexV = new FieldVector3D<>(u, dc1V, v, dc2V, cof1, duV, cof2, dvV);
final FieldVector3D<T> deyP = new FieldVector3D<>(v, dc1P, u.negate(), dc2P, cof1, dvP, cof2.negate(), duP);
final FieldVector3D<T> deyV = new FieldVector3D<>(v, dc1V, u.negate(), dc2V, cof1, dvV, cof2.negate(), duV);
fillHalfRow(one, dexP, jacobian[1], 0);
fillHalfRow(one, dexV, jacobian[1], 3);
fillHalfRow(one, deyP, jacobian[2], 0);
fillHalfRow(one, deyV, jacobian[2], 3);
final T cle = u.divide(a).add(ex).subtract(eSinE.multiply(beta).multiply(ey));
final T sle = v.divide(a).add(ey).add(eSinE.multiply(beta).multiply(ex));
final T m1 = beta.multiply(eCosE);
final T m2 = m1.multiply(eCosE).negate().add(1);
final T m3 = (u.multiply(ey).subtract(v.multiply(ex))).add(eSinE.multiply(beta).multiply(u.multiply(ex).add(v.multiply(ey))));
final T m4 = sle.negate().add(cle.multiply(eSinE).multiply(beta));
final T m5 = cle.add(sle.multiply(eSinE).multiply(beta));
final T kk = m3.multiply(2).divide(r).add(aOr.multiply(eSinE)).add(m1.multiply(eSinE).multiply(m1.add(1).subtract(aOr.add(1).multiply(m2))).divide(epsilon)).divide(r2);
final T jj = (m1.multiply(m2).divide(epsilon).subtract(1)).multiply(oOsqrtMuA);
fillHalfRow(kk, position,
jj, velocity,
m4, dexP,
m5, deyP,
sle.negate().divide(a), duP,
cle.divide(a), dvP,
jacobian[5], 0);
final T ll = (m1.multiply(m2).divide(epsilon ).subtract(1)).multiply(oOsqrtMuA);
final T mm = m3.multiply(2).add(eSinE.multiply(a)).add(m1.multiply(eSinE).multiply(r).multiply(eCosE.multiply(beta).multiply(2).subtract(aOr.multiply(m2))).divide(epsilon)).divide(mu);
fillHalfRow(ll, position,
mm, velocity,
m4, dexV,
m5, deyV,
sle.negate().divide(a), duV,
cle.divide(a), dvV,
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 aM = aE - ex sin aE + ey cos aE leads to:
// daM = (1 - ex cos aE - ey sin aE) dE - sin aE dex + cos aE dey
// which is inverted and rewritten as:
// daE = a/r daM + sin aE a/r dex - cos aE a/r dey
final T alphaE = getAlphaE();
final T cosAe = alphaE.cos();
final T sinAe = alphaE.sin();
final T aOr = one.divide(one.subtract(ex.multiply(cosAe)).subtract(ey.multiply(sinAe)));
// 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 * ( rowL[j] + sinAe * rowEx[j] - cosAe * rowEy[j]);
rowL[j] = aOr.multiply(rowL[j].add(sinAe.multiply(rowEx[j])).subtract( cosAe.multiply(rowEy[j])));
}
jacobian[5] = rowL;
return jacobian;
}
/** {@inheritDoc} */
protected T[][] computeJacobianTrueWrtCartesian() {
// start by computing the Jacobian with eccentric angle
final T[][] jacobian = computeJacobianEccentricWrtCartesian();
// Differentiating the eccentric latitude equation
// tan((aV - aE)/2) = [ex sin aE - ey cos aE] / [sqrt(1-ex^2-ey^2) + 1 - ex cos aE - ey sin aE]
// leads to
// cT (daV - daE) = cE daE + cX dex + cY dey
// with
// cT = [d^2 + (ex sin aE - ey cos aE)^2] / 2
// d = 1 + sqrt(1-ex^2-ey^2) - ex cos aE - ey sin aE
// cE = (ex cos aE + ey sin aE) (sqrt(1-ex^2-ey^2) + 1) - ex^2 - ey^2
// cX = sin aE (sqrt(1-ex^2-ey^2) + 1) - ey + ex (ex sin aE - ey cos aE) / sqrt(1-ex^2-ey^2)
// cY = -cos aE (sqrt(1-ex^2-ey^2) + 1) + ex + ey (ex sin aE - ey cos aE) / sqrt(1-ex^2-ey^2)
// which can be solved to find the differential of the true latitude
// daV = (cT + cE) / cT daE + cX / cT deX + cY / cT deX
final T alphaE = getAlphaE();
final T cosAe = alphaE.cos();
final T sinAe = alphaE.sin();
final T eSinE = ex.multiply(sinAe).subtract(ey.multiply(cosAe));
final T ecosE = ex.multiply(cosAe).add(ey.multiply(sinAe));
final T e2 = ex.multiply(ex).add(ey.multiply(ey));
final T epsilon = (one.subtract(e2)).sqrt();
final T onePeps = one.add(epsilon);
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(sinAe.multiply(onePeps));
final T cY = ey.multiply(eSinE).divide(epsilon).add(ex).subtract(cosAe.multiply(onePeps));
final T factorLe = (cT.add(cE)).divide(cT);
final T factorEx = cX.divide(cT);
final T factorEy = cY.divide(cT);
// update latitude row
final T[] rowEx = jacobian[1];
final T[] rowEy = jacobian[2];
final T[] rowA = jacobian[5];
for (int j = 0; j < 6; ++j) {
rowA[j] = factorLe.multiply(rowA[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 = a.reciprocal().multiply(gm).sqrt().divide(a);
switch (type) {
case MEAN :
pDot[5] = pDot[5].add(n);
break;
case ECCENTRIC :
oMe2 = one.subtract(ex.multiply(ex)).subtract(ey.multiply(ey));
ksi = one.add(ex.multiply(alphaV.cos())).add(ey.multiply(alphaV.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 = one.add(ex.multiply(alphaV.cos())).add(ey.multiply(alphaV.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 Orbit object.
* @return a string representation of this object
*/
public String toString() {
return new StringBuffer().append("circular parameters: ").append('{').
append("a: ").append(a.getReal()).
append(", ex: ").append(ex.getReal()).append(", ey: ").append(ey.getReal()).
append(", i: ").append(FastMath.toDegrees(i.getReal())).
append(", raan: ").append(FastMath.toDegrees(raan.getReal())).
append(", alphaV: ").append(FastMath.toDegrees(alphaV.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
* @deprecated replaced by {@link MathUtils#normalizeAngle(RealFieldElement, RealFieldElement)}
*/
@Deprecated
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 CircularOrbit toOrbit() {
if (hasDerivatives()) {
return new CircularOrbit(a.getReal(), ex.getReal(), ey.getReal(),
i.getReal(), raan.getReal(), alphaV.getReal(),
aDot.getReal(), exDot.getReal(), eyDot.getReal(),
iDot.getReal(), raanDot.getReal(), alphaVDot.getReal(),
PositionAngle.TRUE, getFrame(),
getDate().toAbsoluteDate(), getMu().getReal());
} else {
return new CircularOrbit(a.getReal(), ex.getReal(), ey.getReal(),
i.getReal(), raan.getReal(), alphaV.getReal(),
PositionAngle.TRUE, getFrame(),
getDate().toAbsoluteDate(), getMu().getReal());
}
}
}