EquinoctialLongitudeArgumentUtility.java
/* Copyright 2022-2024 Romain Serra
* 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 org.hipparchus.util.FastMath;
import org.hipparchus.util.SinCos;
import org.orekit.errors.OrekitException;
import org.orekit.errors.OrekitInternalError;
import org.orekit.errors.OrekitMessages;
/**
* Utility methods for converting between different longitude arguments used by {@link EquinoctialOrbit}.
* @author Romain Serra
* @see EquinoctialOrbit
* @since 12.1
*/
public class EquinoctialLongitudeArgumentUtility {
/** Tolerance for stopping criterion in iterative conversion from mean to eccentric angle. */
private static final double TOLERANCE_CONVERGENCE = 1.0e-11;
/** Maximum number of iterations in iterative conversion from mean to eccentric angle. */
private static final int MAXIMUM_ITERATION = 50;
/** Private constructor for utility class. */
private EquinoctialLongitudeArgumentUtility() {
// nothing here (utils class)
}
/**
* Computes the true longitude argument from the eccentric longitude argument.
*
* @param ex e cos(ω), first component of eccentricity vector
* @param ey e sin(ω), second component of eccentricity vector
* @param lE = E + ω + Ω eccentric longitude argument (rad)
* @return the true longitude argument.
*/
public static double eccentricToTrue(final double ex, final double ey, final double lE) {
final double epsilon = eccentricAndTrueEpsilon(ex, ey);
final SinCos scLE = FastMath.sinCos(lE);
final double num = ex * scLE.sin() - ey * scLE.cos();
final double den = epsilon + 1 - ex * scLE.cos() - ey * scLE.sin();
return lE + eccentricAndTrueAtan(num, den);
}
/**
* Computes the eccentric longitude argument from the true longitude argument.
*
* @param ex e cos(ω), first component of eccentricity vector
* @param ey e sin(ω), second component of eccentricity vector
* @param lV = V + ω + Ω true longitude argument (rad)
* @return the eccentric longitude argument.
*/
public static double trueToEccentric(final double ex, final double ey, final double lV) {
final double epsilon = eccentricAndTrueEpsilon(ex, ey);
final SinCos scLv = FastMath.sinCos(lV);
final double num = ey * scLv.cos() - ex * scLv.sin();
final double den = epsilon + 1 + ex * scLv.cos() + ey * scLv.sin();
return lV + eccentricAndTrueAtan(num, den);
}
/**
* Computes an intermediate quantity for conversions between true and eccentric.
*
* @param ex e cos(ω), first component of eccentricity vector
* @param ey e sin(ω), second component of eccentricity vector
* @return intermediate variable referred to as epsilon.
*/
private static double eccentricAndTrueEpsilon(final double ex, final double ey) {
return FastMath.sqrt(1 - ex * ex - ey * ey);
}
/**
* Computes another intermediate quantity for conversions between true and eccentric.
*
* @param num numerator for angular conversion
* @param den denominator for angular conversion
* @return arc-tangent of ratio of inputs times two.
*/
private static double eccentricAndTrueAtan(final double num, final double den) {
return 2. * FastMath.atan(num / den);
}
/**
* Computes the eccentric longitude argument from the mean longitude argument.
*
* @param ex e cos(ω), first component of eccentricity vector
* @param ey e sin(ω), second component of eccentricity vector
* @param lM = M + ω + Ω mean longitude argument (rad)
* @return the eccentric longitude argument.
*/
public static double meanToEccentric(final double ex, final double ey, final double lM) {
// Generalization of Kepler equation to equinoctial parameters
// with lE = PA + RAAN + E and
// lM = PA + RAAN + M = lE - ex.sin(lE) + ey.cos(lE)
double lE = lM;
double shift;
double lEmlM = 0.0;
boolean hasConverged;
int iter = 0;
do {
final SinCos scLE = FastMath.sinCos(lE);
final double f2 = ex * scLE.sin() - ey * scLE.cos();
final double f1 = 1.0 - ex * scLE.cos() - ey * scLE.sin();
final double f0 = lEmlM - f2;
final double f12 = 2.0 * f1;
shift = f0 * f12 / (f1 * f12 - f0 * f2);
lEmlM -= shift;
lE = lM + lEmlM;
hasConverged = FastMath.abs(shift) <= TOLERANCE_CONVERGENCE;
} while (++iter < MAXIMUM_ITERATION && !hasConverged);
if (!hasConverged) {
throw new OrekitException(OrekitMessages.UNABLE_TO_COMPUTE_ECCENTRIC_LONGITUDE_ARGUMENT, iter);
}
return lE;
}
/**
* Computes the mean longitude argument from the eccentric longitude argument.
*
* @param ex e cos(ω), first component of eccentricity vector
* @param ey e sin(ω), second component of eccentricity vector
* @param lE = E + ω + Ω mean longitude argument (rad)
* @return the mean longitude argument.
*/
public static double eccentricToMean(final double ex, final double ey, final double lE) {
final SinCos scLE = FastMath.sinCos(lE);
return lE - ex * scLE.sin() + ey * scLE.cos();
}
/**
* Computes the mean longitude argument from the eccentric longitude argument.
*
* @param ex e cos(ω), first component of eccentricity vector
* @param ey e sin(ω), second component of eccentricity vector
* @param lV = V + ω + Ω true longitude argument (rad)
* @return the mean longitude argument.
*/
public static double trueToMean(final double ex, final double ey, final double lV) {
final double alphaE = trueToEccentric(ex, ey, lV);
return eccentricToMean(ex, ey, alphaE);
}
/**
* Computes the true longitude argument from the eccentric longitude argument.
*
* @param ex e cos(ω), first component of eccentricity vector
* @param ey e sin(ω), second component of eccentricity vector
* @param lM = M + ω + Ω mean longitude argument (rad)
* @return the true longitude argument.
*/
public static double meanToTrue(final double ex, final double ey, final double lM) {
final double alphaE = meanToEccentric(ex, ey, lM);
return eccentricToTrue(ex, ey, alphaE);
}
/**
* Convert argument of longitude.
* @param oldType old position angle type
* @param l old value for argument of longitude
* @param ex ex
* @param ey ey
* @param newType new position angle type
* @return converted argument of longitude
* @since 12.2
*/
public static double convertL(final PositionAngleType oldType, final double l, final double ex,
final double ey, final PositionAngleType newType) {
if (oldType == newType) {
return l;
} else {
switch (newType) {
case ECCENTRIC:
if (oldType == PositionAngleType.MEAN) {
return EquinoctialLongitudeArgumentUtility.meanToEccentric(ex, ey, l);
} else {
return EquinoctialLongitudeArgumentUtility.trueToEccentric(ex, ey, l);
}
case MEAN:
if (oldType == PositionAngleType.TRUE) {
return EquinoctialLongitudeArgumentUtility.trueToMean(ex, ey, l);
} else {
return EquinoctialLongitudeArgumentUtility.eccentricToMean(ex, ey, l);
}
case TRUE:
if (oldType == PositionAngleType.MEAN) {
return EquinoctialLongitudeArgumentUtility.meanToTrue(ex, ey, l);
} else {
return EquinoctialLongitudeArgumentUtility.eccentricToTrue(ex, ey, l);
}
default:
throw new OrekitInternalError(null);
}
}
}
}