CircularLatitudeArgumentUtility.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.OrekitMessages;
/**
* Utility methods for converting between different latitude arguments used by {@link org.orekit.orbits.CircularOrbit}.
* @author Romain Serra
* @see org.orekit.orbits.CircularOrbit
* @since 12.1
*/
public class CircularLatitudeArgumentUtility {
/** Tolerance for stopping criterion in iterative conversion from mean to eccentric angle. */
private static final double TOLERANCE_CONVERGENCE = 1.0e-12;
/** 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 CircularLatitudeArgumentUtility() {
// nothing here (utils class)
}
/**
* Computes the true latitude argument from the eccentric latitude argument.
*
* @param ex e cos(ω), first component of circular eccentricity vector
* @param ey e sin(ω), second component of circular eccentricity vector
* @param alphaE = E + ω eccentric latitude argument (rad)
* @return the true latitude argument.
*/
public static double eccentricToTrue(final double ex, final double ey, final double alphaE) {
final double epsilon = eccentricAndTrueEpsilon(ex, ey);
final SinCos scAlphaE = FastMath.sinCos(alphaE);
final double num = ex * scAlphaE.sin() - ey * scAlphaE.cos();
final double den = epsilon + 1 - ex * scAlphaE.cos() - ey * scAlphaE.sin();
return alphaE + eccentricAndTrueAtan(num, den);
}
/**
* Computes the eccentric latitude argument from the true latitude argument.
*
* @param ex e cos(ω), first component of circular eccentricity vector
* @param ey e sin(ω), second component of circular eccentricity vector
* @param alphaV = V + ω true latitude argument (rad)
* @return the eccentric latitude argument.
*/
public static double trueToEccentric(final double ex, final double ey, final double alphaV) {
final double epsilon = eccentricAndTrueEpsilon(ex, ey);
final SinCos scAlphaV = FastMath.sinCos(alphaV);
final double num = ey * scAlphaV.cos() - ex * scAlphaV.sin();
final double den = epsilon + 1 + ex * scAlphaV.cos() + ey * scAlphaV.sin();
return alphaV + eccentricAndTrueAtan(num, den);
}
/**
* Computes an intermediate quantity for conversions between true and eccentric.
*
* @param ex e cos(ω), first component of circular eccentricity vector
* @param ey e sin(ω), second component of circular 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 latitude argument from the mean latitude argument.
*
* @param ex e cos(ω), first component of circular eccentricity vector
* @param ey e sin(ω), second component of circular eccentricity vector
* @param alphaM = M + ω mean latitude argument (rad)
* @return the eccentric latitude argument.
*/
public static double meanToEccentric(final double ex, final double ey, final double alphaM) {
// Generalization of Kepler equation to circular parameters
// with alphaE = PA + E and
// alphaM = PA + M = alphaE - ex.sin(alphaE) + ey.cos(alphaE)
double alphaE = alphaM;
double shift;
double alphaEMalphaM = 0.0;
boolean hasConverged;
int iter = 0;
do {
final SinCos scAlphaE = FastMath.sinCos(alphaE);
final double f2 = ex * scAlphaE.sin() - ey * scAlphaE.cos();
final double f1 = 1.0 - ex * scAlphaE.cos() - ey * scAlphaE.sin();
final double f0 = alphaEMalphaM - f2;
final double f12 = 2.0 * f1;
shift = f0 * f12 / (f1 * f12 - f0 * f2);
alphaEMalphaM -= shift;
alphaE = alphaM + alphaEMalphaM;
hasConverged = FastMath.abs(shift) <= TOLERANCE_CONVERGENCE;
} while (++iter < MAXIMUM_ITERATION && !hasConverged);
if (!hasConverged) {
throw new OrekitException(OrekitMessages.UNABLE_TO_COMPUTE_ECCENTRIC_LATITUDE_ARGUMENT, iter);
}
return alphaE;
}
/**
* Computes the mean latitude argument from the eccentric latitude argument.
*
* @param ex e cos(ω), first component of circular eccentricity vector
* @param ey e sin(ω), second component of circular eccentricity vector
* @param alphaE = E + ω mean latitude argument (rad)
* @return the mean latitude argument.
*/
public static double eccentricToMean(final double ex, final double ey, final double alphaE) {
final SinCos scAlphaE = FastMath.sinCos(alphaE);
return alphaE + (ey * scAlphaE.cos() - ex * scAlphaE.sin());
}
/**
* Computes the mean latitude argument from the eccentric latitude argument.
*
* @param ex e cos(ω), first component of circular eccentricity vector
* @param ey e sin(ω), second component of circular eccentricity vector
* @param alphaV = V + ω true latitude argument (rad)
* @return the mean latitude argument.
*/
public static double trueToMean(final double ex, final double ey, final double alphaV) {
final double alphaE = trueToEccentric(ex, ey, alphaV);
return eccentricToMean(ex, ey, alphaE);
}
/**
* Computes the true latitude argument from the eccentric latitude argument.
*
* @param ex e cos(ω), first component of circular eccentricity vector
* @param ey e sin(ω), second component of circular eccentricity vector
* @param alphaM = M + ω mean latitude argument (rad)
* @return the true latitude argument.
*/
public static double meanToTrue(final double ex, final double ey, final double alphaM) {
final double alphaE = meanToEccentric(ex, ey, alphaM);
return eccentricToTrue(ex, ey, alphaE);
}
}