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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.
*/
This package provides classes to handle discrete events occurring during
Ordinary Differential Equations integration.
Discrete events detection is based on switching functions. The user provides a simple 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).
When an event is triggered, several different options are available:
- integration can be stopped (this is called a G-stop facility),
- the state vector or the derivatives can be changed,
- or integration can simply go on.
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:
public double g(double t, double[] y) {
return y[0] - targetConcentration;
}
public int eventOccurred(double t, double[] y) {
return STOP;
}
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:
public double g(double t, double[] y) {
return (t - tManeuverStart) ∗ (t - tManeuverStop);
}
public int eventOccurred(double t, double[] y) {
return RESET_DERIVATIVES;
}
The third case is useful mainly for monitoring purposes, a simple example is:
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;
}
/**
*
* <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;