/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF 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.apache.commons.math.ode;
/**
* This class is used in the junit tests for the ODE integrators.
* <p>This specific problem is the following differential equation :
* <pre>
* y1'' = -y1/r^3 y1 (0) = 1-e y1' (0) = 0
* y2'' = -y2/r^3 y2 (0) = 0 y2' (0) =sqrt((1+e)/(1-e))
* r = sqrt (y1^2 + y2^2), e = 0.9
* </pre>
* This is a two-body problem in the plane which can be solved by
* Kepler's equation
* <pre>
* y1 (t) = ...
* </pre>
* </p>
*/
public class TestProblem3
extends TestProblemAbstract {
/** Serializable version identifier. */
private static final long serialVersionUID = 8567328542728919999L;
/** Eccentricity */
double e;
/** theoretical state */
private double[] y;
/**
* Simple constructor.
* @param e eccentricity
*/
public TestProblem3(double e) {
super();
this.e = e;
double[] y0 = { 1 - e, 0, 0, Math.sqrt((1+e)/(1-e)) };
setInitialConditions(0.0, y0);
setFinalConditions(20.0);
double[] errorScale = { 1.0, 1.0, 1.0, 1.0 };
setErrorScale(errorScale);
y = new double[y0.length];
}
/**
* Simple constructor.
*/
public TestProblem3() {
this(0.1);
}
/**
* Copy constructor.
* @param problem problem to copy
*/
public TestProblem3(TestProblem3 problem) {
super(problem);
e = problem.e;
y = problem.y.clone();
}
/** {@inheritDoc} */
public TestProblem3 copy() {
return new TestProblem3(this);
}
@Override
public void doComputeDerivatives(double t, double[] y, double[] yDot) {
// current radius
double r2 = y[0] * y[0] + y[1] * y[1];
double invR3 = 1 / (r2 * Math.sqrt(r2));
// compute the derivatives
yDot[0] = y[2];
yDot[1] = y[3];
yDot[2] = -invR3 * y[0];
yDot[3] = -invR3 * y[1];
}
@Override
public double[] computeTheoreticalState(double t) {
// solve Kepler's equation
double E = t;
double d = 0;
double corr = 999.0;
for (int i = 0; (i < 50) && (Math.abs(corr) > 1.0e-12); ++i) {
double f2 = e * Math.sin(E);
double f0 = d - f2;
double f1 = 1 - e * Math.cos(E);
double f12 = f1 + f1;
corr = f0 * f12 / (f1 * f12 - f0 * f2);
d -= corr;
E = t + d;
};
double cosE = Math.cos(E);
double sinE = Math.sin(E);
y[0] = cosE - e;
y[1] = Math.sqrt(1 - e * e) * sinE;
y[2] = -sinE / (1 - e * cosE);
y[3] = Math.sqrt(1 - e * e) * cosE / (1 - e * cosE);
return y;
}
}
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