1 /*
2 * Licensed to the Apache Software Foundation (ASF) under one or more
3 * contributor license agreements. See the NOTICE file distributed with
4 * this work for additional information regarding copyright ownership.
5 * The ASF licenses this file to You under the Apache License, Version 2.0
6 * (the "License"); you may not use this file except in compliance with
7 * the License. You may obtain a copy of the License at
8 *
9 * http://www.apache.org/licenses/LICENSE-2.0
10 *
11 * Unless required by applicable law or agreed to in writing, software
12 * distributed under the License is distributed on an "AS IS" BASIS,
13 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
14 * See the License for the specific language governing permissions and
15 * limitations under the License.
16 */
17
18 package org.apache.commons.math.ode;
19
20 /**
21 * This class is used in the junit tests for the ODE integrators.
22
23 * <p>This specific problem is the following differential equation :
24 * <pre>
25 * y1'' = -y1/r^3 y1 (0) = 1-e y1' (0) = 0
26 * y2'' = -y2/r^3 y2 (0) = 0 y2' (0) =sqrt((1+e)/(1-e))
27 * r = sqrt (y1^2 + y2^2), e = 0.9
28 * </pre>
29 * This is a two-body problem in the plane which can be solved by
30 * Kepler's equation
31 * <pre>
32 * y1 (t) = ...
33 * </pre>
34 * </p>
35
36 */
37 public class TestProblem3
38 extends TestProblemAbstract {
39
40 /** Serializable version identifier. */
41 private static final long serialVersionUID = 8567328542728919999L;
42
43 /** Eccentricity */
44 double e;
45
46 /** theoretical state */
47 private double[] y;
48
49 /**
50 * Simple constructor.
51 * @param e eccentricity
52 */
53 public TestProblem3(double e) {
54 super();
55 this.e = e;
56 double[] y0 = { 1 - e, 0, 0, Math.sqrt((1+e)/(1-e)) };
57 setInitialConditions(0.0, y0);
58 setFinalConditions(20.0);
59 double[] errorScale = { 1.0, 1.0, 1.0, 1.0 };
60 setErrorScale(errorScale);
61 y = new double[y0.length];
62 }
63
64 /**
65 * Simple constructor.
66 */
67 public TestProblem3() {
68 this(0.1);
69 }
70
71 /**
72 * Copy constructor.
73 * @param problem problem to copy
74 */
75 public TestProblem3(TestProblem3 problem) {
76 super(problem);
77 e = problem.e;
78 y = problem.y.clone();
79 }
80
81 /** {@inheritDoc} */
82 public TestProblem3 copy() {
83 return new TestProblem3(this);
84 }
85
86 @Override
87 public void doComputeDerivatives(double t, double[] y, double[] yDot) {
88
89 // current radius
90 double r2 = y[0] * y[0] + y[1] * y[1];
91 double invR3 = 1 / (r2 * Math.sqrt(r2));
92
93 // compute the derivatives
94 yDot[0] = y[2];
95 yDot[1] = y[3];
96 yDot[2] = -invR3 * y[0];
97 yDot[3] = -invR3 * y[1];
98
99 }
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 }