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 class TestProblem3
38 extends TestProblemAbstract {
39
40 /** Eccentricity */
41 double e;
42
43 /** theoretical state */
44 private double[] y;
45
46 /**
47 * Simple constructor.
48 * @param e eccentricity
49 */
50 public TestProblem3(double e) {
51 super();
52 this.e = e;
53 double[] y0 = { 1 - e, 0, 0, Math.sqrt((1+e)/(1-e)) };
54 setInitialConditions(0.0, y0);
55 setFinalConditions(20.0);
56 double[] errorScale = { 1.0, 1.0, 1.0, 1.0 };
57 setErrorScale(errorScale);
58 y = new double[y0.length];
59 }
60
61 /**
62 * Simple constructor.
63 */
64 public TestProblem3() {
65 this(0.1);
66 }
67
68 /**
69 * Copy constructor.
70 * @param problem problem to copy
71 */
72 public TestProblem3(TestProblem3 problem) {
73 super(problem);
74 e = problem.e;
75 y = (double[]) problem.y.clone();
76 }
77
78 /**
79 * Clone operation.
80 * @return a copy of the instance
81 */
82 public Object clone() {
83 return new TestProblem3(this);
84 }
85
86 public void doComputeDerivatives(double t, double[] y, double[] yDot) {
87
88 // current radius
89 double r2 = y[0] * y[0] + y[1] * y[1];
90 double invR3 = 1 / (r2 * Math.sqrt(r2));
91
92 // compute the derivatives
93 yDot[0] = y[2];
94 yDot[1] = y[3];
95 yDot[2] = -invR3 * y[0];
96 yDot[3] = -invR3 * y[1];
97
98 }
99
100 public double[] computeTheoreticalState(double t) {
101
102 // solve Kepler's equation
103 double E = t;
104 double d = 0;
105 double corr = 0;
106 do {
107 double f2 = e * Math.sin(E);
108 double f0 = d - f2;
109 double f1 = 1 - e * Math.cos(E);
110 double f12 = f1 + f1;
111 corr = f0 * f12 / (f1 * f12 - f0 * f2);
112 d -= corr;
113 E = t + d;
114 } while (Math.abs(corr) > 1.0e-12);
115
116 double cosE = Math.cos(E);
117 double sinE = Math.sin(E);
118
119 y[0] = cosE - e;
120 y[1] = Math.sqrt(1 - e * e) * sinE;
121 y[2] = -sinE / (1 - e * cosE);
122 y[3] = Math.sqrt(1 - e * e) * cosE / (1 - e * cosE);
123
124 return y;
125 }
126
127 }