FieldCircularLatitudeArgumentUtility.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.CalculusFieldElement;
import org.hipparchus.util.FastMath;
import org.hipparchus.util.FieldSinCos;
import org.orekit.errors.OrekitException;
import org.orekit.errors.OrekitMessages;
/**
* Utility methods for converting between different latitude arguments used by {@link FieldCircularOrbit}.
* @author Romain Serra
* @see FieldCircularOrbit
* @since 12.1
*/
public class FieldCircularLatitudeArgumentUtility {
/** 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 FieldCircularLatitudeArgumentUtility() {
// nothing here (utils class)
}
/**
* Computes the true latitude argument from the eccentric latitude argument.
*
* @param <T> Type of the field elements
* @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 <T extends CalculusFieldElement<T>> T eccentricToTrue(final T ex, final T ey, final T alphaE) {
final T epsilon = eccentricAndTrueEpsilon(ex, ey);
final FieldSinCos<T> scAlphaE = FastMath.sinCos(alphaE);
final T cosAlphaE = scAlphaE.cos();
final T sinAlphaE = scAlphaE.sin();
final T num = ex.multiply(sinAlphaE).subtract(ey.multiply(cosAlphaE));
final T den = epsilon.add(1).subtract(ex.multiply(cosAlphaE)).subtract(ey.multiply(sinAlphaE));
return alphaE.add(eccentricAndTrueAtan(num, den));
}
/**
* Computes the eccentric latitude argument from the true latitude argument.
*
* @param <T> Type of the field elements
* @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 <T extends CalculusFieldElement<T>> T trueToEccentric(final T ex, final T ey, final T alphaV) {
final T epsilon = eccentricAndTrueEpsilon(ex, ey);
final FieldSinCos<T> scAlphaV = FastMath.sinCos(alphaV);
final T cosAlphaV = scAlphaV.cos();
final T sinAlphaV = scAlphaV.sin();
final T num = ey.multiply(cosAlphaV).subtract(ex.multiply(sinAlphaV));
final T den = epsilon.add(1).add(ex.multiply(cosAlphaV).add(ey.multiply(sinAlphaV)));
return alphaV.add(eccentricAndTrueAtan(num, den));
}
/**
* Computes an intermediate quantity for conversions between true and eccentric.
*
* @param <T> Type of the field elements
* @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 <T extends CalculusFieldElement<T>> T eccentricAndTrueEpsilon(final T ex, final T ey) {
return (ex.square().negate().subtract(ey.square()).add(1.)).sqrt();
}
/**
* Computes another intermediate quantity for conversions between true and eccentric.
*
* @param <T> Type of the field elements
* @param num numerator for angular conversion
* @param den denominator for angular conversion
* @return arc-tangent of ratio of inputs times two.
*/
private static <T extends CalculusFieldElement<T>> T eccentricAndTrueAtan(final T num, final T den) {
return (num.divide(den)).atan().multiply(2);
}
/**
* Computes the eccentric latitude argument from the mean latitude argument.
*
* @param <T> Type of the field elements
* @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 <T extends CalculusFieldElement<T>> T meanToEccentric(final T ex, final T ey, final T alphaM) {
// 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;
T alphaEMalphaM = alphaM.getField().getZero();
boolean hasConverged;
int iter = 0;
do {
final FieldSinCos<T> scAlphaE = FastMath.sinCos(alphaE);
final T f2 = ex.multiply(scAlphaE.sin()).subtract(ey.multiply(scAlphaE.cos()));
final T f1 = ex.negate().multiply(scAlphaE.cos()).subtract(ey.multiply(scAlphaE.sin())).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);
hasConverged = FastMath.abs(shift.getReal()) <= 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 <T> Type of the field elements
* @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 mean latitude argument.
*/
public static <T extends CalculusFieldElement<T>> T eccentricToMean(final T ex, final T ey, final T alphaE) {
final FieldSinCos<T> scAlphaE = FastMath.sinCos(alphaE);
return alphaE.subtract(ex.multiply(scAlphaE.sin()).subtract(ey.multiply(scAlphaE.cos())));
}
/**
* Computes the mean latitude argument from the eccentric latitude argument.
*
* @param <T> Type of the field elements
* @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 <T extends CalculusFieldElement<T>> T trueToMean(final T ex, final T ey, final T alphaV) {
final T alphaE = trueToEccentric(ex, ey, alphaV);
return eccentricToMean(ex, ey, alphaE);
}
/**
* Computes the true latitude argument from the eccentric latitude argument.
*
* @param <T> Type of the field elements
* @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 <T extends CalculusFieldElement<T>> T meanToTrue(final T ex, final T ey, final T alphaM) {
final T alphaE = meanToEccentric(ex, ey, alphaM);
return eccentricToTrue(ex, ey, alphaE);
}
}