CircularOrbit.java
/* Copyright 2002-2024 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
* limitations under the License.
*/
package org.orekit.orbits;
import java.io.Serializable;
import org.hipparchus.analysis.differentiation.UnivariateDerivative1;
import org.hipparchus.geometry.euclidean.threed.Vector3D;
import org.hipparchus.util.FastMath;
import org.hipparchus.util.SinCos;
import org.orekit.annotation.DefaultDataContext;
import org.orekit.errors.OrekitIllegalArgumentException;
import org.orekit.errors.OrekitInternalError;
import org.orekit.errors.OrekitMessages;
import org.orekit.frames.Frame;
import org.orekit.frames.KinematicTransform;
import org.orekit.time.AbsoluteDate;
import org.orekit.time.TimeOffset;
import org.orekit.utils.PVCoordinates;
import org.orekit.utils.TimeStampedPVCoordinates;
/**
* 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
*/
public class CircularOrbit extends Orbit implements PositionAngleBased<CircularOrbit> {
/** Serializable UID. */
private static final long serialVersionUID = 20231217L;
/** Semi-major axis (m). */
private final double a;
/** First component of the circular eccentricity vector. */
private final double ex;
/** Second component of the circular eccentricity vector. */
private final double ey;
/** Inclination (rad). */
private final double i;
/** Right Ascension of Ascending Node (rad). */
private final double raan;
/** Cached latitude argument (rad). */
private final double cachedAlpha;
/** Type of cached position angle (latitude argument). */
private final PositionAngleType cachedPositionAngleType;
/** Semi-major axis derivative (m/s). */
private final double aDot;
/** First component of the circular eccentricity vector derivative. */
private final double exDot;
/** Second component of the circular eccentricity vector derivative. */
private final double eyDot;
/** Inclination derivative (rad/s). */
private final double iDot;
/** Right Ascension of Ascending Node derivative (rad/s). */
private final double raanDot;
/** True latitude argument derivative (rad/s). */
private final double cachedAlphaDot;
/** Indicator for {@link PVCoordinates} serialization. */
private final boolean serializePV;
/** Partial Cartesian coordinates (position and velocity are valid, acceleration may be missing). */
private transient PVCoordinates partialPV;
/** 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 cachedPositionAngleType type of cached 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}
* @since 12.1
*/
public CircularOrbit(final double a, final double ex, final double ey,
final double i, final double raan, final double alpha,
final PositionAngleType type, final PositionAngleType cachedPositionAngleType,
final Frame frame, final AbsoluteDate date, final double mu)
throws IllegalArgumentException {
this(a, ex, ey, i, raan, alpha, 0., 0., 0., 0., 0.,
computeKeplerianAlphaDot(type, a, ex, ey, mu, alpha, type),
type, cachedPositionAngleType, frame, date, mu);
}
/** Creates a new instance without derivatives and with cached position angle same as value inputted.
* @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 CircularOrbit(final double a, final double ex, final double ey,
final double i, final double raan, final double alpha,
final PositionAngleType type,
final Frame frame, final AbsoluteDate date, final double mu)
throws IllegalArgumentException {
this(a, ex, ey, i, raan, alpha, type, 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 cachedPositionAngleType type of cached 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}
* @since 12.1
*/
public CircularOrbit(final double a, final double ex, final double ey,
final double i, final double raan, final double alpha,
final double aDot, final double exDot, final double eyDot,
final double iDot, final double raanDot, final double alphaDot,
final PositionAngleType type, final PositionAngleType cachedPositionAngleType,
final Frame frame, final AbsoluteDate date, final double mu)
throws IllegalArgumentException {
super(frame, date, mu);
if (ex * ex + ey * ey >= 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;
this.cachedPositionAngleType = cachedPositionAngleType;
final UnivariateDerivative1 alphaUD = initializeCachedAlpha(alpha, alphaDot, type);
this.cachedAlpha = alphaUD.getValue();
this.cachedAlphaDot = alphaUD.getFirstDerivative();
serializePV = false;
partialPV = null;
}
/** Creates a new instance with derivatives and with cached position angle same as value inputted.
* @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 CircularOrbit(final double a, final double ex, final double ey,
final double i, final double raan, final double alpha,
final double aDot, final double exDot, final double eyDot,
final double iDot, final double raanDot, final double alphaDot,
final PositionAngleType type,
final Frame frame, final AbsoluteDate date, final double mu)
throws IllegalArgumentException {
this(a, ex, ey, i, raan, alpha, aDot, exDot, eyDot, iDot, raanDot, alphaDot, type, 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 input 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 input latitude argument derivative (rad/s)
* @param pvCoordinates the {@link PVCoordinates} in inertial frame
* @param positionAngleType type of position angle
* @param frame the frame in which are defined the parameters
* (<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}
*/
private CircularOrbit(final double a, final double ex, final double ey,
final double i, final double raan, final double alpha,
final double aDot, final double exDot, final double eyDot,
final double iDot, final double raanDot, final double alphaDot,
final TimeStampedPVCoordinates pvCoordinates,
final PositionAngleType positionAngleType, final Frame frame, final double mu)
throws IllegalArgumentException {
super(pvCoordinates, frame, mu);
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;
this.cachedAlpha = alpha;
this.cachedAlphaDot = alphaDot;
this.cachedPositionAngleType = positionAngleType;
this.serializePV = true;
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(double)} and {@link #getPVCoordinates(AbsoluteDate, Frame)}.
*
* @param pvCoordinates the {@link PVCoordinates} in inertial frame
* @param frame the frame in which are defined the {@link PVCoordinates}
* (<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 CircularOrbit(final TimeStampedPVCoordinates pvCoordinates, final Frame frame, final double mu)
throws IllegalArgumentException {
super(pvCoordinates, frame, mu);
this.cachedPositionAngleType = PositionAngleType.TRUE;
// compute semi-major axis
final Vector3D pvP = pvCoordinates.getPosition();
final Vector3D pvV = pvCoordinates.getVelocity();
final Vector3D pvA = pvCoordinates.getAcceleration();
final double r2 = pvP.getNormSq();
final double r = FastMath.sqrt(r2);
final double V2 = pvV.getNormSq();
final double rV2OnMu = r * V2 / mu;
a = r / (2 - rV2OnMu);
if (!isElliptical()) {
throw new OrekitIllegalArgumentException(OrekitMessages.HYPERBOLIC_ORBIT_NOT_HANDLED_AS,
getClass().getName());
}
// compute inclination
final Vector3D momentum = pvCoordinates.getMomentum();
i = Vector3D.angle(momentum, Vector3D.PLUS_K);
// compute right ascension of ascending node
final Vector3D node = Vector3D.crossProduct(Vector3D.PLUS_K, momentum);
raan = FastMath.atan2(node.getY(), node.getX());
// 2D-coordinates in the canonical frame
final SinCos scRaan = FastMath.sinCos(raan);
final SinCos scI = FastMath.sinCos(i);
final double xP = pvP.getX();
final double yP = pvP.getY();
final double zP = pvP.getZ();
final double x2 = (xP * scRaan.cos() + yP * scRaan.sin()) / a;
final double y2 = ((yP * scRaan.cos() - xP * scRaan.sin()) * scI.cos() + zP * scI.sin()) / a;
// compute eccentricity vector
final double eSE = Vector3D.dotProduct(pvP, pvV) / FastMath.sqrt(mu * a);
final double eCE = rV2OnMu - 1;
final double e2 = eCE * eCE + eSE * eSE;
final double f = eCE - e2;
final double g = FastMath.sqrt(1 - e2) * eSE;
final double aOnR = a / r;
final double a2OnR2 = aOnR * aOnR;
ex = a2OnR2 * (f * x2 + g * y2);
ey = a2OnR2 * (f * y2 - g * x2);
// compute latitude argument
final double beta = 1 / (1 + FastMath.sqrt(1 - ex * ex - ey * ey));
cachedAlpha = CircularLatitudeArgumentUtility.eccentricToTrue(ex, ey, FastMath.atan2(y2 + ey + eSE * beta * ex, x2 + ex - eSE * beta * ey));
partialPV = pvCoordinates;
if (hasNonKeplerianAcceleration(pvCoordinates, mu)) {
// we have a relevant acceleration, we can compute derivatives
final double[][] jacobian = new double[6][6];
getJacobianWrtCartesian(PositionAngleType.MEAN, jacobian);
final Vector3D keplerianAcceleration = new Vector3D(-mu / (r * r2), pvP);
final Vector3D nonKeplerianAcceleration = pvA.subtract(keplerianAcceleration);
final double aX = nonKeplerianAcceleration.getX();
final double aY = nonKeplerianAcceleration.getY();
final double aZ = nonKeplerianAcceleration.getZ();
aDot = jacobian[0][3] * aX + jacobian[0][4] * aY + jacobian[0][5] * aZ;
exDot = jacobian[1][3] * aX + jacobian[1][4] * aY + jacobian[1][5] * aZ;
eyDot = jacobian[2][3] * aX + jacobian[2][4] * aY + jacobian[2][5] * aZ;
iDot = jacobian[3][3] * aX + jacobian[3][4] * aY + jacobian[3][5] * aZ;
raanDot = jacobian[4][3] * aX + jacobian[4][4] * aY + jacobian[4][5] * aZ;
// in order to compute latitude argument derivative, we must compute
// mean latitude argument derivative including Keplerian motion and convert to true latitude argument
final double alphaMDot = getKeplerianMeanMotion() +
jacobian[5][3] * aX + jacobian[5][4] * aY + jacobian[5][5] * aZ;
final UnivariateDerivative1 exUD = new UnivariateDerivative1(ex, exDot);
final UnivariateDerivative1 eyUD = new UnivariateDerivative1(ey, eyDot);
final UnivariateDerivative1 alphaMUD = new UnivariateDerivative1(getAlphaM(), alphaMDot);
final UnivariateDerivative1 alphavUD = FieldCircularLatitudeArgumentUtility.meanToTrue(exUD, eyUD, alphaMUD);
cachedAlphaDot = alphavUD.getFirstDerivative();
} else {
// acceleration is either almost zero or NaN,
// we assume acceleration was not known
// we don't set up derivatives
aDot = 0.;
exDot = 0.;
eyDot = 0.;
iDot = 0.;
raanDot = 0.;
cachedAlphaDot = computeKeplerianAlphaDot(cachedPositionAngleType, a, ex, ey, mu, cachedAlpha, cachedPositionAngleType);
}
serializePV = true;
}
/** 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(double)} and {@link #getPVCoordinates(AbsoluteDate, Frame)}.
*
* @param pvCoordinates the {@link PVCoordinates} in inertial frame
* @param frame the frame in which are defined the {@link PVCoordinates}
* (<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 CircularOrbit(final PVCoordinates pvCoordinates, final Frame frame,
final AbsoluteDate date, final double mu)
throws IllegalArgumentException {
this(new TimeStampedPVCoordinates(date, pvCoordinates), frame, mu);
}
/** Constructor from any kind of orbital parameters.
* @param op orbital parameters to copy
*/
public CircularOrbit(final Orbit op) {
super(op.getFrame(), op.getDate(), op.getMu());
a = op.getA();
i = op.getI();
final double hx = op.getHx();
final double hy = op.getHy();
final double h2 = hx * hx + hy * hy;
final double h = FastMath.sqrt(h2);
raan = FastMath.atan2(hy, hx);
final SinCos scRaan = FastMath.sinCos(raan);
final double cosRaan = h == 0 ? scRaan.cos() : hx / h;
final double sinRaan = h == 0 ? scRaan.sin() : hy / h;
final double equiEx = op.getEquinoctialEx();
final double equiEy = op.getEquinoctialEy();
ex = equiEx * cosRaan + equiEy * sinRaan;
ey = equiEy * cosRaan - equiEx * sinRaan;
cachedPositionAngleType = PositionAngleType.TRUE;
cachedAlpha = op.getLv() - raan;
if (op.hasNonKeplerianAcceleration()) {
aDot = op.getADot();
final double hxDot = op.getHxDot();
final double hyDot = op.getHyDot();
iDot = 2 * (cosRaan * hxDot + sinRaan * hyDot) / (1 + h2);
raanDot = (hx * hyDot - hy * hxDot) / h2;
final double equiExDot = op.getEquinoctialExDot();
final double equiEyDot = op.getEquinoctialEyDot();
exDot = (equiExDot + equiEy * raanDot) * cosRaan +
(equiEyDot - equiEx * raanDot) * sinRaan;
eyDot = (equiEyDot - equiEx * raanDot) * cosRaan -
(equiExDot + equiEy * raanDot) * sinRaan;
cachedAlphaDot = op.getLvDot() - raanDot;
} else {
aDot = 0.;
exDot = 0.;
eyDot = 0.;
iDot = 0.;
raanDot = 0.;
cachedAlphaDot = computeKeplerianAlphaDot(cachedPositionAngleType, a, ex, ey, getMu(), cachedAlpha, cachedPositionAngleType);
}
serializePV = false;
partialPV = null;
}
/** {@inheritDoc} */
@Override
public boolean hasNonKeplerianAcceleration() {
return aDot != 0. || exDot != 0. || eyDot != 0. || iDot != 0. || raanDot != 0. ||
FastMath.abs(cachedAlphaDot - computeKeplerianAlphaDot(cachedPositionAngleType, a, ex, ey, getMu(), cachedAlpha, cachedPositionAngleType)) > TOLERANCE_POSITION_ANGLE_RATE;
}
/** {@inheritDoc} */
@Override
public OrbitType getType() {
return OrbitType.CIRCULAR;
}
/** {@inheritDoc} */
@Override
public double getA() {
return a;
}
/** {@inheritDoc} */
@Override
public double getADot() {
return aDot;
}
/** {@inheritDoc} */
@Override
public double getEquinoctialEx() {
final SinCos sc = FastMath.sinCos(raan);
return ex * sc.cos() - ey * sc.sin();
}
/** {@inheritDoc} */
@Override
public double getEquinoctialExDot() {
if (!hasNonKeplerianAcceleration()) {
return 0.;
}
final SinCos sc = FastMath.sinCos(raan);
return (exDot - ey * raanDot) * sc.cos() - (eyDot + ex * raanDot) * sc.sin();
}
/** {@inheritDoc} */
@Override
public double getEquinoctialEy() {
final SinCos sc = FastMath.sinCos(raan);
return ey * sc.cos() + ex * sc.sin();
}
/** {@inheritDoc} */
@Override
public double getEquinoctialEyDot() {
if (!hasNonKeplerianAcceleration()) {
return 0.;
}
final SinCos sc = FastMath.sinCos(raan);
return (eyDot + ex * raanDot) * sc.cos() + (exDot - ey * raanDot) * sc.sin();
}
/** Get the first component of the circular eccentricity vector.
* @return ex = e cos(ω), first component of the circular eccentricity vector
*/
public double getCircularEx() {
return ex;
}
/** Get the first component of the circular eccentricity vector derivative.
* @return ex = e cos(ω), first component of the circular eccentricity vector derivative
* @since 9.0
*/
public double 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 double getCircularEy() {
return ey;
}
/** Get the second component of the circular eccentricity vector derivative.
* @return ey = e sin(ω), second component of the circular eccentricity vector derivative
*/
public double getCircularEyDot() {
return eyDot;
}
/** {@inheritDoc} */
@Override
public double getHx() {
// Check for equatorial retrograde orbit
if (FastMath.abs(i - FastMath.PI) < 1.0e-10) {
return Double.NaN;
}
return FastMath.cos(raan) * FastMath.tan(i / 2);
}
/** {@inheritDoc} */
@Override
public double getHxDot() {
// Check for equatorial retrograde orbit
if (FastMath.abs(i - FastMath.PI) < 1.0e-10) {
return Double.NaN;
}
if (!hasNonKeplerianAcceleration()) {
return 0.;
}
final SinCos sc = FastMath.sinCos(raan);
final double tan = FastMath.tan(0.5 * i);
return 0.5 * sc.cos() * (1 + tan * tan) * iDot - sc.sin() * tan * raanDot;
}
/** {@inheritDoc} */
@Override
public double getHy() {
// Check for equatorial retrograde orbit
if (FastMath.abs(i - FastMath.PI) < 1.0e-10) {
return Double.NaN;
}
return FastMath.sin(raan) * FastMath.tan(i / 2);
}
/** {@inheritDoc} */
@Override
public double getHyDot() {
// Check for equatorial retrograde orbit
if (FastMath.abs(i - FastMath.PI) < 1.0e-10) {
return Double.NaN;
}
if (!hasNonKeplerianAcceleration()) {
return 0.;
}
final SinCos sc = FastMath.sinCos(raan);
final double tan = FastMath.tan(0.5 * i);
return 0.5 * sc.sin() * (1 + tan * tan) * iDot + sc.cos() * tan * raanDot;
}
/** Get the true latitude argument.
* @return v + ω true latitude argument (rad)
*/
public double getAlphaV() {
switch (cachedPositionAngleType) {
case TRUE:
return cachedAlpha;
case ECCENTRIC:
return CircularLatitudeArgumentUtility.eccentricToTrue(ex, ey, cachedAlpha);
case MEAN:
return CircularLatitudeArgumentUtility.meanToTrue(ex, ey, cachedAlpha);
default:
throw new OrekitInternalError(null);
}
}
/** Get the true latitude argument derivative.
* <p>
* If the orbit was created without derivatives, the value returned is {@link Double#NaN}.
* </p>
* @return v + ω true latitude argument derivative (rad/s)
* @since 9.0
*/
public double getAlphaVDot() {
switch (cachedPositionAngleType) {
case ECCENTRIC:
final UnivariateDerivative1 alphaEUD = new UnivariateDerivative1(cachedAlpha, cachedAlphaDot);
final UnivariateDerivative1 exUD = new UnivariateDerivative1(ex, exDot);
final UnivariateDerivative1 eyUD = new UnivariateDerivative1(ey, eyDot);
final UnivariateDerivative1 alphaVUD = FieldCircularLatitudeArgumentUtility.eccentricToTrue(exUD, eyUD,
alphaEUD);
return alphaVUD.getFirstDerivative();
case TRUE:
return cachedAlphaDot;
case MEAN:
final UnivariateDerivative1 alphaMUD = new UnivariateDerivative1(cachedAlpha, cachedAlphaDot);
final UnivariateDerivative1 exUD2 = new UnivariateDerivative1(ex, exDot);
final UnivariateDerivative1 eyUD2 = new UnivariateDerivative1(ey, eyDot);
final UnivariateDerivative1 alphaVUD2 = FieldCircularLatitudeArgumentUtility.meanToTrue(exUD2,
eyUD2, alphaMUD);
return alphaVUD2.getFirstDerivative();
default:
throw new OrekitInternalError(null);
}
}
/** Get the eccentric latitude argument.
* @return E + ω eccentric latitude argument (rad)
*/
public double getAlphaE() {
switch (cachedPositionAngleType) {
case TRUE:
return CircularLatitudeArgumentUtility.trueToEccentric(ex, ey, cachedAlpha);
case ECCENTRIC:
return cachedAlpha;
case MEAN:
return CircularLatitudeArgumentUtility.meanToEccentric(ex, ey, cachedAlpha);
default:
throw new OrekitInternalError(null);
}
}
/** Get the eccentric latitude argument derivative.
* <p>
* If the orbit was created without derivatives, the value returned is {@link Double#NaN}.
* </p>
* @return d(E + ω)/dt eccentric latitude argument derivative (rad/s)
* @since 9.0
*/
public double getAlphaEDot() {
switch (cachedPositionAngleType) {
case TRUE:
final UnivariateDerivative1 alphaVUD = new UnivariateDerivative1(cachedAlpha, cachedAlphaDot);
final UnivariateDerivative1 exUD = new UnivariateDerivative1(ex, exDot);
final UnivariateDerivative1 eyUD = new UnivariateDerivative1(ey, eyDot);
final UnivariateDerivative1 alphaEUD = FieldCircularLatitudeArgumentUtility.trueToEccentric(exUD, eyUD,
alphaVUD);
return alphaEUD.getFirstDerivative();
case ECCENTRIC:
return cachedAlphaDot;
case MEAN:
final UnivariateDerivative1 alphaMUD = new UnivariateDerivative1(cachedAlpha, cachedAlphaDot);
final UnivariateDerivative1 exUD2 = new UnivariateDerivative1(ex, exDot);
final UnivariateDerivative1 eyUD2 = new UnivariateDerivative1(ey, eyDot);
final UnivariateDerivative1 alphaVUD2 = FieldCircularLatitudeArgumentUtility.meanToEccentric(exUD2,
eyUD2, alphaMUD);
return alphaVUD2.getFirstDerivative();
default:
throw new OrekitInternalError(null);
}
}
/** Get the mean latitude argument.
* @return M + ω mean latitude argument (rad)
*/
public double getAlphaM() {
switch (cachedPositionAngleType) {
case TRUE:
return CircularLatitudeArgumentUtility.trueToMean(ex, ey, cachedAlpha);
case MEAN:
return cachedAlpha;
case ECCENTRIC:
return CircularLatitudeArgumentUtility.eccentricToMean(ex, ey, cachedAlpha);
default:
throw new OrekitInternalError(null);
}
}
/** Get the mean latitude argument derivative.
* <p>
* If the orbit was created without derivatives, the value returned is {@link Double#NaN}.
* </p>
* @return d(M + ω)/dt mean latitude argument derivative (rad/s)
* @since 9.0
*/
public double getAlphaMDot() {
switch (cachedPositionAngleType) {
case TRUE:
final UnivariateDerivative1 alphaVUD = new UnivariateDerivative1(cachedAlpha, cachedAlphaDot);
final UnivariateDerivative1 exUD = new UnivariateDerivative1(ex, exDot);
final UnivariateDerivative1 eyUD = new UnivariateDerivative1(ey, eyDot);
final UnivariateDerivative1 alphaMUD = FieldCircularLatitudeArgumentUtility.trueToMean(exUD, eyUD,
alphaVUD);
return alphaMUD.getFirstDerivative();
case MEAN:
return cachedAlphaDot;
case ECCENTRIC:
final UnivariateDerivative1 alphaEUD = new UnivariateDerivative1(cachedAlpha, cachedAlphaDot);
final UnivariateDerivative1 exUD2 = new UnivariateDerivative1(ex, exDot);
final UnivariateDerivative1 eyUD2 = new UnivariateDerivative1(ey, eyDot);
final UnivariateDerivative1 alphaMUD2 = FieldCircularLatitudeArgumentUtility.eccentricToMean(exUD2,
eyUD2, alphaEUD);
return alphaMUD2.getFirstDerivative();
default:
throw new OrekitInternalError(null);
}
}
/** Get the latitude argument.
* @param type type of the angle
* @return latitude argument (rad)
*/
public double getAlpha(final PositionAngleType type) {
return (type == PositionAngleType.MEAN) ? getAlphaM() :
((type == PositionAngleType.ECCENTRIC) ? getAlphaE() :
getAlphaV());
}
/** Get the latitude argument derivative.
* <p>
* If the orbit was created without derivatives, the value returned is {@link Double#NaN}.
* </p>
* @param type type of the angle
* @return latitude argument derivative (rad/s)
* @since 9.0
*/
public double getAlphaDot(final PositionAngleType type) {
return (type == PositionAngleType.MEAN) ? getAlphaMDot() :
((type == PositionAngleType.ECCENTRIC) ? getAlphaEDot() :
getAlphaVDot());
}
/** {@inheritDoc} */
@Override
public double getE() {
return FastMath.sqrt(ex * ex + ey * ey);
}
/** {@inheritDoc} */
@Override
public double getEDot() {
if (!hasNonKeplerianAcceleration()) {
return 0.;
}
return (ex * exDot + ey * eyDot) / getE();
}
/** {@inheritDoc} */
@Override
public double getI() {
return i;
}
/** {@inheritDoc} */
@Override
public double getIDot() {
return iDot;
}
/** Get the right ascension of the ascending node.
* @return right ascension of the ascending node (rad)
*/
public double getRightAscensionOfAscendingNode() {
return raan;
}
/** Get the right ascension of the ascending node derivative.
* <p>
* If the orbit was created without derivatives, the value returned is {@link Double#NaN}.
* </p>
* @return right ascension of the ascending node derivative (rad/s)
* @since 9.0
*/
public double getRightAscensionOfAscendingNodeDot() {
return raanDot;
}
/** {@inheritDoc} */
@Override
public double getLv() {
return getAlphaV() + raan;
}
/** {@inheritDoc} */
@Override
public double getLvDot() {
return getAlphaVDot() + raanDot;
}
/** {@inheritDoc} */
@Override
public double getLE() {
return getAlphaE() + raan;
}
/** {@inheritDoc} */
@Override
public double getLEDot() {
return getAlphaEDot() + raanDot;
}
/** {@inheritDoc} */
@Override
public double getLM() {
return getAlphaM() + raan;
}
/** {@inheritDoc} */
@Override
public double getLMDot() {
return getAlphaMDot() + raanDot;
}
/** Compute position and velocity but not acceleration.
*/
private void computePVWithoutA() {
if (partialPV != null) {
// already computed
return;
}
// get equinoctial parameters
final double equEx = getEquinoctialEx();
final double equEy = getEquinoctialEy();
final double hx = getHx();
final double hy = getHy();
final double lE = getLE();
// inclination-related intermediate parameters
final double hx2 = hx * hx;
final double hy2 = hy * hy;
final double factH = 1. / (1 + hx2 + hy2);
// reference axes defining the orbital plane
final double ux = (1 + hx2 - hy2) * factH;
final double uy = 2 * hx * hy * factH;
final double uz = -2 * hy * factH;
final double vx = uy;
final double vy = (1 - hx2 + hy2) * factH;
final double vz = 2 * hx * factH;
// eccentricity-related intermediate parameters
final double exey = equEx * equEy;
final double ex2 = equEx * equEx;
final double ey2 = equEy * equEy;
final double e2 = ex2 + ey2;
final double eta = 1 + FastMath.sqrt(1 - e2);
final double beta = 1. / eta;
// eccentric latitude argument
final SinCos scLe = FastMath.sinCos(lE);
final double cLe = scLe.cos();
final double sLe = scLe.sin();
final double exCeyS = equEx * cLe + equEy * sLe;
// coordinates of position and velocity in the orbital plane
final double x = a * ((1 - beta * ey2) * cLe + beta * exey * sLe - equEx);
final double y = a * ((1 - beta * ex2) * sLe + beta * exey * cLe - equEy);
final double factor = FastMath.sqrt(getMu() / a) / (1 - exCeyS);
final double xdot = factor * (-sLe + beta * equEy * exCeyS);
final double ydot = factor * ( cLe - beta * equEx * exCeyS);
final Vector3D position =
new Vector3D(x * ux + y * vx, x * uy + y * vy, x * uz + y * vz);
final Vector3D velocity =
new Vector3D(xdot * ux + ydot * vx, xdot * uy + ydot * vy, xdot * uz + ydot * vz);
partialPV = new PVCoordinates(position, velocity);
}
/** Initialize cached alpha with rate.
* @param alpha input alpha
* @param alphaDot rate of input alpha
* @param inputType position angle type passed as input
* @return alpha to cache with rate
* @since 12.1
*/
private UnivariateDerivative1 initializeCachedAlpha(final double alpha, final double alphaDot,
final PositionAngleType inputType) {
if (cachedPositionAngleType == inputType) {
return new UnivariateDerivative1(alpha, alphaDot);
} else {
final UnivariateDerivative1 exUD = new UnivariateDerivative1(ex, exDot);
final UnivariateDerivative1 eyUD = new UnivariateDerivative1(ey, eyDot);
final UnivariateDerivative1 alphaUD = new UnivariateDerivative1(alpha, alphaDot);
switch (cachedPositionAngleType) {
case ECCENTRIC:
if (inputType == PositionAngleType.MEAN) {
return FieldCircularLatitudeArgumentUtility.meanToEccentric(exUD, eyUD, alphaUD);
} else {
return FieldCircularLatitudeArgumentUtility.trueToEccentric(exUD, eyUD, alphaUD);
}
case TRUE:
if (inputType == PositionAngleType.MEAN) {
return FieldCircularLatitudeArgumentUtility.meanToTrue(exUD, eyUD, alphaUD);
} else {
return FieldCircularLatitudeArgumentUtility.eccentricToTrue(exUD, eyUD, alphaUD);
}
case MEAN:
if (inputType == PositionAngleType.TRUE) {
return FieldCircularLatitudeArgumentUtility.trueToMean(exUD, eyUD, alphaUD);
} else {
return FieldCircularLatitudeArgumentUtility.eccentricToMean(exUD, eyUD, alphaUD);
}
default:
throw new OrekitInternalError(null);
}
}
}
/** Compute non-Keplerian part of the acceleration from first time derivatives.
* @return non-Keplerian part of the acceleration
*/
private Vector3D nonKeplerianAcceleration() {
final double[][] dCdP = new double[6][6];
getJacobianWrtParameters(PositionAngleType.MEAN, dCdP);
final double nonKeplerianMeanMotion = getAlphaMDot() - getKeplerianMeanMotion();
final double nonKeplerianAx = dCdP[3][0] * aDot + dCdP[3][1] * exDot + dCdP[3][2] * eyDot +
dCdP[3][3] * iDot + dCdP[3][4] * raanDot + dCdP[3][5] * nonKeplerianMeanMotion;
final double nonKeplerianAy = dCdP[4][0] * aDot + dCdP[4][1] * exDot + dCdP[4][2] * eyDot +
dCdP[4][3] * iDot + dCdP[4][4] * raanDot + dCdP[4][5] * nonKeplerianMeanMotion;
final double nonKeplerianAz = dCdP[5][0] * aDot + dCdP[5][1] * exDot + dCdP[5][2] * eyDot +
dCdP[5][3] * iDot + dCdP[5][4] * raanDot + dCdP[5][5] * nonKeplerianMeanMotion;
return new Vector3D(nonKeplerianAx, nonKeplerianAy, nonKeplerianAz);
}
/** {@inheritDoc} */
@Override
protected Vector3D initPosition() {
// get equinoctial parameters
final double equEx = getEquinoctialEx();
final double equEy = getEquinoctialEy();
final double hx = getHx();
final double hy = getHy();
final double lE = getLE();
// inclination-related intermediate parameters
final double hx2 = hx * hx;
final double hy2 = hy * hy;
final double factH = 1. / (1 + hx2 + hy2);
// reference axes defining the orbital plane
final double ux = (1 + hx2 - hy2) * factH;
final double uy = 2 * hx * hy * factH;
final double uz = -2 * hy * factH;
final double vx = uy;
final double vy = (1 - hx2 + hy2) * factH;
final double vz = 2 * hx * factH;
// eccentricity-related intermediate parameters
final double exey = equEx * equEy;
final double ex2 = equEx * equEx;
final double ey2 = equEy * equEy;
final double e2 = ex2 + ey2;
final double eta = 1 + FastMath.sqrt(1 - e2);
final double beta = 1. / eta;
// eccentric latitude argument
final SinCos scLe = FastMath.sinCos(lE);
final double cLe = scLe.cos();
final double sLe = scLe.sin();
// coordinates of position and velocity in the orbital plane
final double x = a * ((1 - beta * ey2) * cLe + beta * exey * sLe - equEx);
final double y = a * ((1 - beta * ex2) * sLe + beta * exey * cLe - equEy);
return new Vector3D(x * ux + y * vx, x * uy + y * vy, x * uz + y * vz);
}
/** {@inheritDoc} */
@Override
protected TimeStampedPVCoordinates initPVCoordinates() {
// position and velocity
computePVWithoutA();
// acceleration
final double r2 = partialPV.getPosition().getNormSq();
final Vector3D keplerianAcceleration = new Vector3D(-getMu() / (r2 * FastMath.sqrt(r2)), partialPV.getPosition());
final Vector3D acceleration = hasNonKeplerianRates() ?
keplerianAcceleration.add(nonKeplerianAcceleration()) :
keplerianAcceleration;
return new TimeStampedPVCoordinates(getDate(), partialPV.getPosition(), partialPV.getVelocity(), acceleration);
}
/** {@inheritDoc} */
@Override
public CircularOrbit withFrame(final Frame inertialFrame) {
final PVCoordinates pvCoordinates;
if (hasNonKeplerianAcceleration()) {
pvCoordinates = getPVCoordinates(inertialFrame);
} else {
final KinematicTransform transform = getFrame().getKinematicTransformTo(inertialFrame, getDate());
pvCoordinates = transform.transformOnlyPV(getPVCoordinates());
}
final CircularOrbit circularOrbit = new CircularOrbit(pvCoordinates, inertialFrame, getDate(), getMu());
if (circularOrbit.getCachedPositionAngleType() == getCachedPositionAngleType()) {
return circularOrbit;
} else {
return circularOrbit.withCachedPositionAngleType(getCachedPositionAngleType());
}
}
/** {@inheritDoc} */
@Override
public CircularOrbit withCachedPositionAngleType(final PositionAngleType positionAngleType) {
return new CircularOrbit(a, ex, ey, i, raan, getAlpha(positionAngleType), aDot, exDot, eyDot, iDot, raanDot,
getAlphaDot(positionAngleType), positionAngleType, getFrame(), getDate(), getMu());
}
/** {@inheritDoc} */
@Override
public CircularOrbit shiftedBy(final double dt) {
return shiftedBy(new TimeOffset(dt));
}
/** {@inheritDoc} */
@Override
public CircularOrbit shiftedBy(final TimeOffset dt) {
final double dtS = dt.toDouble();
// use Keplerian-only motion
final CircularOrbit keplerianShifted = new CircularOrbit(a, ex, ey, i, raan,
getAlphaM() + getKeplerianMeanMotion() * dtS,
PositionAngleType.MEAN, cachedPositionAngleType,
getFrame(), getDate().shiftedBy(dt), getMu());
if (hasNonKeplerianRates()) {
// extract non-Keplerian acceleration from first time derivatives
final Vector3D nonKeplerianAcceleration = nonKeplerianAcceleration();
// add quadratic effect of non-Keplerian acceleration to Keplerian-only shift
keplerianShifted.computePVWithoutA();
final Vector3D fixedP = new Vector3D(1, keplerianShifted.partialPV.getPosition(),
0.5 * dtS * dtS, nonKeplerianAcceleration);
final double fixedR2 = fixedP.getNormSq();
final double fixedR = FastMath.sqrt(fixedR2);
final Vector3D fixedV = new Vector3D(1, keplerianShifted.partialPV.getVelocity(),
dtS, nonKeplerianAcceleration);
final Vector3D fixedA = new Vector3D(-getMu() / (fixedR2 * fixedR), keplerianShifted.partialPV.getPosition(),
1, nonKeplerianAcceleration);
// build a new orbit, taking non-Keplerian acceleration into account
return new CircularOrbit(new TimeStampedPVCoordinates(keplerianShifted.getDate(),
fixedP, fixedV, fixedA),
keplerianShifted.getFrame(), keplerianShifted.getMu());
} else {
// Keplerian-only motion is all we can do
return keplerianShifted;
}
}
/** {@inheritDoc} */
@Override
protected double[][] computeJacobianMeanWrtCartesian() {
final double[][] jacobian = new double[6][6];
computePVWithoutA();
final Vector3D position = partialPV.getPosition();
final Vector3D velocity = partialPV.getVelocity();
final double x = position.getX();
final double y = position.getY();
final double z = position.getZ();
final double vx = velocity.getX();
final double vy = velocity.getY();
final double vz = velocity.getZ();
final double pv = Vector3D.dotProduct(position, velocity);
final double r2 = position.getNormSq();
final double r = FastMath.sqrt(r2);
final double v2 = velocity.getNormSq();
final double mu = getMu();
final double oOsqrtMuA = 1 / FastMath.sqrt(mu * a);
final double rOa = r / a;
final double aOr = a / r;
final double aOr2 = a / r2;
final double a2 = a * a;
final double ex2 = ex * ex;
final double ey2 = ey * ey;
final double e2 = ex2 + ey2;
final double epsilon = FastMath.sqrt(1 - e2);
final double beta = 1 / (1 + epsilon);
final double eCosE = 1 - rOa;
final double eSinE = pv * oOsqrtMuA;
final SinCos scI = FastMath.sinCos(i);
final SinCos scRaan = FastMath.sinCos(raan);
final double cosI = scI.cos();
final double sinI = scI.sin();
final double cosRaan = scRaan.cos();
final double sinRaan = scRaan.sin();
// da
fillHalfRow(2 * aOr * aOr2, position, jacobian[0], 0);
fillHalfRow(2 * a2 / mu, velocity, jacobian[0], 3);
// differentials of the normalized momentum
final Vector3D danP = new Vector3D(v2, position, -pv, velocity);
final Vector3D danV = new Vector3D(r2, velocity, -pv, position);
final double recip = 1 / partialPV.getMomentum().getNorm();
final double recip2 = recip * recip;
final Vector3D dwXP = new Vector3D(recip, new Vector3D( 0, vz, -vy), -recip2 * sinRaan * sinI, danP);
final Vector3D dwYP = new Vector3D(recip, new Vector3D(-vz, 0, vx), recip2 * cosRaan * sinI, danP);
final Vector3D dwZP = new Vector3D(recip, new Vector3D( vy, -vx, 0), -recip2 * cosI, danP);
final Vector3D dwXV = new Vector3D(recip, new Vector3D( 0, -z, y), -recip2 * sinRaan * sinI, danV);
final Vector3D dwYV = new Vector3D(recip, new Vector3D( z, 0, -x), recip2 * cosRaan * sinI, danV);
final Vector3D dwZV = new Vector3D(recip, new Vector3D( -y, x, 0), -recip2 * cosI, danV);
// di
fillHalfRow(sinRaan * cosI, dwXP, -cosRaan * cosI, dwYP, -sinI, dwZP, jacobian[3], 0);
fillHalfRow(sinRaan * cosI, dwXV, -cosRaan * cosI, dwYV, -sinI, dwZV, jacobian[3], 3);
// dRaan
fillHalfRow(sinRaan / sinI, dwYP, cosRaan / sinI, dwXP, jacobian[4], 0);
fillHalfRow(sinRaan / sinI, dwYV, cosRaan / 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 double u = x * cosRaan + y * sinRaan;
final double cv = -x * sinRaan + y * cosRaan;
final double v = cv * cosI + z * sinI;
// du
final Vector3D duP = new Vector3D(cv * cosRaan / sinI, dwXP,
cv * sinRaan / sinI, dwYP,
1, new Vector3D(cosRaan, sinRaan, 0));
final Vector3D duV = new Vector3D(cv * cosRaan / sinI, dwXV,
cv * sinRaan / sinI, dwYV);
// dv
final Vector3D dvP = new Vector3D(-u * cosRaan * cosI / sinI + sinRaan * z, dwXP,
-u * sinRaan * cosI / sinI - cosRaan * z, dwYP,
cv, dwZP,
1, new Vector3D(-sinRaan * cosI, cosRaan * cosI, sinI));
final Vector3D dvV = new Vector3D(-u * cosRaan * cosI / sinI + sinRaan * z, dwXV,
-u * sinRaan * cosI / sinI - cosRaan * z, dwYV,
cv, dwZV);
final Vector3D dc1P = new Vector3D(aOr2 * (2 * eSinE * eSinE + 1 - eCosE) / r2, position,
-2 * aOr2 * eSinE * oOsqrtMuA, velocity);
final Vector3D dc1V = new Vector3D(-2 * aOr2 * eSinE * oOsqrtMuA, position,
2 / mu, velocity);
final Vector3D dc2P = new Vector3D(aOr2 * eSinE * (eSinE * eSinE - (1 - e2)) / (r2 * epsilon), position,
aOr2 * (1 - e2 - eSinE * eSinE) * oOsqrtMuA / epsilon, velocity);
final Vector3D dc2V = new Vector3D(aOr2 * (1 - e2 - eSinE * eSinE) * oOsqrtMuA / epsilon, position,
eSinE / (mu * epsilon), velocity);
final double cof1 = aOr2 * (eCosE - e2);
final double cof2 = aOr2 * epsilon * eSinE;
final Vector3D dexP = new Vector3D(u, dc1P, v, dc2P, cof1, duP, cof2, dvP);
final Vector3D dexV = new Vector3D(u, dc1V, v, dc2V, cof1, duV, cof2, dvV);
final Vector3D deyP = new Vector3D(v, dc1P, -u, dc2P, cof1, dvP, -cof2, duP);
final Vector3D deyV = new Vector3D(v, dc1V, -u, dc2V, cof1, dvV, -cof2, duV);
fillHalfRow(1, dexP, jacobian[1], 0);
fillHalfRow(1, dexV, jacobian[1], 3);
fillHalfRow(1, deyP, jacobian[2], 0);
fillHalfRow(1, deyV, jacobian[2], 3);
final double cle = u / a + ex - eSinE * beta * ey;
final double sle = v / a + ey + eSinE * beta * ex;
final double m1 = beta * eCosE;
final double m2 = 1 - m1 * eCosE;
final double m3 = (u * ey - v * ex) + eSinE * beta * (u * ex + v * ey);
final double m4 = -sle + cle * eSinE * beta;
final double m5 = cle + sle * eSinE * beta;
fillHalfRow((2 * m3 / r + aOr * eSinE + m1 * eSinE * (1 + m1 - (1 + aOr) * m2) / epsilon) / r2, position,
(m1 * m2 / epsilon - 1) * oOsqrtMuA, velocity,
m4, dexP, m5, deyP, -sle / a, duP, cle / a, dvP,
jacobian[5], 0);
fillHalfRow((m1 * m2 / epsilon - 1) * oOsqrtMuA, position,
(2 * m3 + eSinE * a + m1 * eSinE * r * (eCosE * beta * 2 - aOr * m2) / epsilon) / mu, velocity,
m4, dexV, m5, deyV, -sle / a, duV, cle / a, dvV,
jacobian[5], 3);
return jacobian;
}
/** {@inheritDoc} */
@Override
protected double[][] computeJacobianEccentricWrtCartesian() {
// start by computing the Jacobian with mean angle
final double[][] jacobian = computeJacobianMeanWrtCartesian();
// Differentiating the Kepler equation aM = aE - ex sin aE + ey cos aE leads to:
// daM = (1 - ex cos aE - ey sin aE) daE - 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 double alphaE = getAlphaE();
final SinCos scAe = FastMath.sinCos(alphaE);
final double cosAe = scAe.cos();
final double sinAe = scAe.sin();
final double aOr = 1 / (1 - ex * cosAe - ey * sinAe);
// update longitude row
final double[] rowEx = jacobian[1];
final double[] rowEy = jacobian[2];
final double[] rowL = jacobian[5];
for (int j = 0; j < 6; ++j) {
rowL[j] = aOr * (rowL[j] + sinAe * rowEx[j] - cosAe * rowEy[j]);
}
return jacobian;
}
/** {@inheritDoc} */
@Override
protected double[][] computeJacobianTrueWrtCartesian() {
// start by computing the Jacobian with eccentric angle
final double[][] 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 double alphaE = getAlphaE();
final SinCos scAe = FastMath.sinCos(alphaE);
final double cosAe = scAe.cos();
final double sinAe = scAe.sin();
final double eSinE = ex * sinAe - ey * cosAe;
final double ecosE = ex * cosAe + ey * sinAe;
final double e2 = ex * ex + ey * ey;
final double epsilon = FastMath.sqrt(1 - e2);
final double onePeps = 1 + epsilon;
final double d = onePeps - ecosE;
final double cT = (d * d + eSinE * eSinE) / 2;
final double cE = ecosE * onePeps - e2;
final double cX = ex * eSinE / epsilon - ey + sinAe * onePeps;
final double cY = ey * eSinE / epsilon + ex - cosAe * onePeps;
final double factorLe = (cT + cE) / cT;
final double factorEx = cX / cT;
final double factorEy = cY / cT;
// update latitude row
final double[] rowEx = jacobian[1];
final double[] rowEy = jacobian[2];
final double[] rowA = jacobian[5];
for (int j = 0; j < 6; ++j) {
rowA[j] = factorLe * rowA[j] + factorEx * rowEx[j] + factorEy * rowEy[j];
}
return jacobian;
}
/** {@inheritDoc} */
@Override
public void addKeplerContribution(final PositionAngleType type, final double gm,
final double[] pDot) {
pDot[5] += computeKeplerianAlphaDot(type, a, ex, ey, gm, cachedAlpha, cachedPositionAngleType);
}
/**
* Compute rate of argument of latitude.
* @param type position angle type of rate
* @param a semi major axis
* @param ex ex
* @param ey ey
* @param mu mu
* @param alpha argument of latitude
* @param cachedType position angle type of passed alpha
* @return first-order time derivative for alpha
* @since 12.2
*/
private static double computeKeplerianAlphaDot(final PositionAngleType type, final double a, final double ex,
final double ey, final double mu,
final double alpha, final PositionAngleType cachedType) {
final double n = FastMath.sqrt(mu / a) / a;
if (type == PositionAngleType.MEAN) {
return n;
}
final double ksi;
final SinCos sc;
if (type == PositionAngleType.ECCENTRIC) {
sc = FastMath.sinCos(CircularLatitudeArgumentUtility.convertAlpha(cachedType, alpha, ex, ey, type));
ksi = 1. / (1 - ex * sc.cos() - ey * sc.sin());
return n * ksi;
} else { // TRUE
sc = FastMath.sinCos(CircularLatitudeArgumentUtility.convertAlpha(cachedType, alpha, ex, ey, type));
final double oMe2 = 1 - ex * ex - ey * ey;
ksi = 1 + ex * sc.cos() + ey * sc.sin();
return n * ksi * ksi / (oMe2 * FastMath.sqrt(oMe2));
}
}
/** Returns a string representation of this Orbit object.
* @return a string representation of this object
*/
public String toString() {
return new StringBuilder().append("circular parameters: ").append('{').
append("a: ").append(a).
append(", ex: ").append(ex).append(", ey: ").append(ey).
append(", i: ").append(FastMath.toDegrees(i)).
append(", raan: ").append(FastMath.toDegrees(raan)).
append(", alphaV: ").append(FastMath.toDegrees(getAlphaV())).
append(";}").toString();
}
/** {@inheritDoc} */
@Override
public PositionAngleType getCachedPositionAngleType() {
return cachedPositionAngleType;
}
/** {@inheritDoc} */
@Override
public boolean hasNonKeplerianRates() {
return hasNonKeplerianAcceleration();
}
/** {@inheritDoc} */
@Override
public CircularOrbit withKeplerianRates() {
final PositionAngleType positionAngleType = getCachedPositionAngleType();
return new CircularOrbit(a, ex, ey, i, raan, cachedAlpha, positionAngleType, positionAngleType,
getFrame(), getDate(), getMu());
}
/** Replace the instance with a data transfer object for serialization.
* @return data transfer object that will be serialized
*/
@DefaultDataContext
private Object writeReplace() {
return new DTO(this);
}
/** Internal class used only for serialization. */
@DefaultDataContext
private static class DTO implements Serializable {
/** Serializable UID. */
private static final long serialVersionUID = 20241114L;
/** Seconds. */
private final long seconds;
/** Attoseconds. */
private final long attoseconds;
/** Double values. */
private final double[] d;
/** Frame in which are defined the orbital parameters. */
private final Frame frame;
/** Type of cached position angle. */
private final PositionAngleType positionAngleType;
/** Simple constructor.
* @param orbit instance to serialize
*/
private DTO(final CircularOrbit orbit) {
positionAngleType = orbit.getCachedPositionAngleType();
// decompose date
this.seconds = orbit.getDate().getSeconds();
this.attoseconds = orbit.getDate().getAttoSeconds();
if (orbit.serializePV) {
final TimeStampedPVCoordinates pv = orbit.getPVCoordinates();
this.d = new double[] {
// mu + orbit + derivatives + Cartesian : 22 parameters
orbit.getMu(),
orbit.a, orbit.ex, orbit.ey,
orbit.i, orbit.raan, orbit.cachedAlpha,
orbit.aDot, orbit.exDot, orbit.eyDot,
orbit.iDot, orbit.raanDot, orbit.cachedAlphaDot,
pv.getPosition().getX(), pv.getPosition().getY(), pv.getPosition().getZ(),
pv.getVelocity().getX(), pv.getVelocity().getY(), pv.getVelocity().getZ(),
pv.getAcceleration().getX(), pv.getAcceleration().getY(), pv.getAcceleration().getZ(),
};
} else {
// mu + orbit + derivatives: 13 parameters
this.d = new double[] {
orbit.getMu(),
orbit.a, orbit.ex, orbit.ey,
orbit.i, orbit.raan, orbit.cachedAlpha,
orbit.aDot, orbit.exDot, orbit.eyDot,
orbit.iDot, orbit.raanDot, orbit.cachedAlphaDot
};
}
this.frame = orbit.getFrame();
}
/** Replace the deserialized data transfer object with a {@link CircularOrbit}.
* @return replacement {@link CircularOrbit}
*/
private Object readResolve() {
if (d.length == 22) { // mu + orbit + derivatives + Cartesian
return new CircularOrbit(d[1], d[2], d[3], d[4], d[5], d[6],
d[7], d[8], d[9], d[10], d[11], d[12],
new TimeStampedPVCoordinates(new AbsoluteDate(new TimeOffset(seconds, attoseconds)),
new Vector3D(d[13], d[14], d[15]),
new Vector3D(d[16], d[17], d[18]),
new Vector3D(d[19], d[20], d[21])),
positionAngleType, frame,
d[0]);
}
return new CircularOrbit(d[1], d[2], d[3], d[4], d[5], d[6],
d[7], d[8], d[9], d[10], d[11], d[12],
positionAngleType, positionAngleType,
frame, new AbsoluteDate(new TimeOffset(seconds, attoseconds)),
d[0]);
}
}
}