ClohessyWiltshireEquations.java
/* Copyright 2002-2026 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.propagation.relative.clohessywiltshire;
import org.hipparchus.linear.MatrixUtils;
import org.hipparchus.util.FastMath;
import org.hipparchus.util.SinCos;
/**
* This class implements the state transition matrices of the Clohessy-Wiltshire equations of relative motion between
* two spacecraft. Source : Orbital Mechanics for Engineering Students, Curtis, chapter 7
*
* @author Jérôme Tabeaud
* @author Romain Cuvillon
* @since 14.0
*/
public class ClohessyWiltshireEquations {
/**
* Private constructor to prevent instantiation.
*/
private ClohessyWiltshireEquations() {
}
/**
* Computes the state transition matrices at the given time since epoch.
*
* @param timeSinceEpoch Time since epoch, given in seconds
* @param meanMotion Mean motion of the target's CIRCULAR orbit
* @return 4 3x3 state transition matrices
*/
public static ClohessyWiltshireMatrices computeMatrices(final double timeSinceEpoch, final double meanMotion) {
final double nt = meanMotion * timeSinceEpoch;
final SinCos sinCos_nt = FastMath.sinCos(nt);
final double sin_nt = sinCos_nt.sin();
final double cos_nt = sinCos_nt.cos();
// Position and velocity state transition matrices
final double[][] phi_rr = { {4.0 - 3 * cos_nt, 0.0, 0.0}, {6.0 * (sin_nt - nt), 1.0, 0.0}, {0.0, 0.0, cos_nt} };
final double[][] phi_rv = {
{(1.0 / meanMotion) * sin_nt, (2.0 / meanMotion) * (1.0 - cos_nt), 0.0},
{(2.0 / meanMotion) * (cos_nt - 1.0), (1.0 / meanMotion) * (4.0 * sin_nt - 3.0 * nt), 0.0},
{0.0, 0.0, (1 / meanMotion) * sin_nt}
};
final double[][] phi_vr = {
{3.0 * meanMotion * sin_nt, 0.0, 0.0}, {6.0 * meanMotion * (cos_nt - 1), 0.0, 0.0},
{0.0, 0.0, -meanMotion * sin_nt}
};
final double[][] phi_vv = {
{cos_nt, 2.0 * sin_nt, 0.0}, {-2.0 * sin_nt, 4.0 * cos_nt - 3.0, 0.0}, {0.0, 0.0, cos_nt}
};
return new ClohessyWiltshireMatrices(timeSinceEpoch, MatrixUtils.createRealMatrix(phi_rr),
MatrixUtils.createRealMatrix(phi_rv), MatrixUtils.createRealMatrix(phi_vr),
MatrixUtils.createRealMatrix(phi_vv));
}
}