src/main/java/org/apache/commons/math/ode/events/package.html - platform/external/apache-commons-math - Git at Google

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 <body>
 <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.math.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>

 </body>
 </html>
	<html>
	<!--
	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.
	-->
	<!-- $Revision: 613620 $ -->
	<body>
	<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.math.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>

	</body>
	</html>