001 /*
002 * Licensed to the Apache Software Foundation (ASF) under one or more
003 * contributor license agreements. See the NOTICE file distributed with
004 * this work for additional information regarding copyright ownership.
005 * The ASF licenses this file to You under the Apache License, Version 2.0
006 * (the "License"); you may not use this file except in compliance with
007 * the License. You may obtain a copy of the License at
008 *
009 * http://www.apache.org/licenses/LICENSE-2.0
010 *
011 * Unless required by applicable law or agreed to in writing, software
012 * distributed under the License is distributed on an "AS IS" BASIS,
013 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
014 * See the License for the specific language governing permissions and
015 * limitations under the License.
016 */
017
018 package org.apache.commons.math.ode;
019
020 /**
021 * This class is used in the junit tests for the ODE integrators.
022
023 * <p>This specific problem is the following differential equation :
024 * <pre>
025 * y1'' = -y1/r^3 y1 (0) = 1-e y1' (0) = 0
026 * y2'' = -y2/r^3 y2 (0) = 0 y2' (0) =sqrt((1+e)/(1-e))
027 * r = sqrt (y1^2 + y2^2), e = 0.9
028 * </pre>
029 * This is a two-body problem in the plane which can be solved by
030 * Kepler's equation
031 * <pre>
032 * y1 (t) = ...
033 * </pre>
034 * </p>
035
036 */
037 public class TestProblem3
038 extends TestProblemAbstract {
039
040 /** Serializable version identifier. */
041 private static final long serialVersionUID = 8567328542728919999L;
042
043 /** Eccentricity */
044 double e;
045
046 /** theoretical state */
047 private double[] y;
048
049 /**
050 * Simple constructor.
051 * @param e eccentricity
052 */
053 public TestProblem3(double e) {
054 super();
055 this.e = e;
056 double[] y0 = { 1 - e, 0, 0, Math.sqrt((1+e)/(1-e)) };
057 setInitialConditions(0.0, y0);
058 setFinalConditions(20.0);
059 double[] errorScale = { 1.0, 1.0, 1.0, 1.0 };
060 setErrorScale(errorScale);
061 y = new double[y0.length];
062 }
063
064 /**
065 * Simple constructor.
066 */
067 public TestProblem3() {
068 this(0.1);
069 }
070
071 /**
072 * Copy constructor.
073 * @param problem problem to copy
074 */
075 public TestProblem3(TestProblem3 problem) {
076 super(problem);
077 e = problem.e;
078 y = problem.y.clone();
079 }
080
081 /** {@inheritDoc} */
082 public TestProblem3 copy() {
083 return new TestProblem3(this);
084 }
085
086 @Override
087 public void doComputeDerivatives(double t, double[] y, double[] yDot) {
088
089 // current radius
090 double r2 = y[0] * y[0] + y[1] * y[1];
091 double invR3 = 1 / (r2 * Math.sqrt(r2));
092
093 // compute the derivatives
094 yDot[0] = y[2];
095 yDot[1] = y[3];
096 yDot[2] = -invR3 * y[0];
097 yDot[3] = -invR3 * y[1];
098
099 }
100
101 @Override
102 public double[] computeTheoreticalState(double t) {
103
104 // solve Kepler's equation
105 double E = t;
106 double d = 0;
107 double corr = 999.0;
108 for (int i = 0; (i < 50) && (Math.abs(corr) > 1.0e-12); ++i) {
109 double f2 = e * Math.sin(E);
110 double f0 = d - f2;
111 double f1 = 1 - e * Math.cos(E);
112 double f12 = f1 + f1;
113 corr = f0 * f12 / (f1 * f12 - f0 * f2);
114 d -= corr;
115 E = t + d;
116 };
117
118 double cosE = Math.cos(E);
119 double sinE = Math.sin(E);
120
121 y[0] = cosE - e;
122 y[1] = Math.sqrt(1 - e * e) * sinE;
123 y[2] = -sinE / (1 - e * cosE);
124 y[3] = Math.sqrt(1 - e * e) * cosE / (1 - e * cosE);
125
126 return y;
127 }
128
129 }