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* 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.
*/
/**
*
* <p>
* This package provides classes to handle discrete events occurring during
* Ordinary Differential Equations integration.
* </p>
*
* <p>
* Discrete events detection is based on switching functions. The user provides
* a simple {@link org.apache.commons.math3.ode.events.EventHandler#g g(t, y)}
* function depending on the current time and state. The integrator will monitor
* the value of the function throughout integration range and will trigger the
* event when its sign changes. The magnitude of the value is almost irrelevant,
* it should however be continuous (but not necessarily smooth) for the sake of
* root finding. The steps are shortened as needed to ensure the events occur
* at step boundaries (even if the integrator is a fixed-step integrator).
* </p>
*
* <p>
* When an event is triggered, several different options are available:
* </p>
* <ul>
* <li>integration can be stopped (this is called a G-stop facility),</li>
* <li>the state vector or the derivatives can be changed,</li>
* <li>or integration can simply go on.</li>
* </ul>
*
* <p>
* The first case, G-stop, is the most common one. A typical use case is when an
* ODE must be solved up to some target state is reached, with a known value of
* the state but an unknown occurrence time. As an example, if we want to monitor
* a chemical reaction up to some predefined concentration for the first substance,
* we can use the following switching function setting:
* <pre>
* public double g(double t, double[] y) {
* return y[0] - targetConcentration;
* }
*
* public int eventOccurred(double t, double[] y) {
* return STOP;
* }
* </pre>
* </p>
*
* <p>
* The second case, change state vector or derivatives is encountered when dealing
* with discontinuous dynamical models. A typical case would be the motion of a
* spacecraft when thrusters are fired for orbital maneuvers. The acceleration is
* smooth as long as no maneuver are performed, depending only on gravity, drag,
* third body attraction, radiation pressure. Firing a thruster introduces a
* discontinuity that must be handled appropriately by the integrator. In such a case,
* we would use a switching function setting similar to this:
* <pre>
* public double g(double t, double[] y) {
* return (t - tManeuverStart) ∗ (t - tManeuverStop);
* }
*
* public int eventOccurred(double t, double[] y) {
* return RESET_DERIVATIVES;
* }
* </pre>
* </p>
*
* <p>
* The third case is useful mainly for monitoring purposes, a simple example is:
* <pre>
* public double g(double t, double[] y) {
* return y[0] - y[1];
* }
*
* public int eventOccurred(double t, double[] y) {
* logger.log("y0(t) and y1(t) curves cross at t = " + t);
* return CONTINUE;
* }
* </pre>
* </p>
*
*
*/
package org.apache.commons.math3.ode.events;