| /* |
| * 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.math3.ode; |
| |
| import org.apache.commons.math3.util.FastMath; |
| |
| /** |
| * 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 { |
| |
| /** 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, FastMath.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); |
| } |
| |
| @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 * FastMath.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) && (FastMath.abs(corr) > 1.0e-12); ++i) { |
| double f2 = e * FastMath.sin(E); |
| double f0 = d - f2; |
| double f1 = 1 - e * FastMath.cos(E); |
| double f12 = f1 + f1; |
| corr = f0 * f12 / (f1 * f12 - f0 * f2); |
| d -= corr; |
| E = t + d; |
| } |
| |
| double cosE = FastMath.cos(E); |
| double sinE = FastMath.sin(E); |
| |
| y[0] = cosE - e; |
| y[1] = FastMath.sqrt(1 - e * e) * sinE; |
| y[2] = -sinE / (1 - e * cosE); |
| y[3] = FastMath.sqrt(1 - e * e) * cosE / (1 - e * cosE); |
| |
| return y; |
| } |
| |
| } |