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| <h1 title="Package" class="title">Package org.apache.commons.math3.ode.events</h1> |
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| <div class="block"> |
| This package provides classes to handle discrete events occurring during |
| Ordinary Differential Equations integration.</div> |
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| <p>See: <a href="#package_description">Description</a></p> |
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| <td class="colFirst"><a href="../../../../../../org/apache/commons/math3/ode/events/EventHandler.html" title="interface in org.apache.commons.math3.ode.events">EventHandler</a></td> |
| <td class="colLast"> |
| <div class="block">This interface represents a handler for discrete events triggered |
| during ODE integration.</div> |
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| <td class="colFirst"><a href="../../../../../../org/apache/commons/math3/ode/events/EventFilter.html" title="class in org.apache.commons.math3.ode.events">EventFilter</a></td> |
| <td class="colLast"> |
| <div class="block">Wrapper used to detect only increasing or decreasing events.</div> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <td class="colFirst"><a href="../../../../../../org/apache/commons/math3/ode/events/EventState.html" title="class in org.apache.commons.math3.ode.events">EventState</a></td> |
| <td class="colLast"> |
| <div class="block">This class handles the state for one <a href="../../../../../../org/apache/commons/math3/ode/events/EventHandler.html" title="interface in org.apache.commons.math3.ode.events"><code>event handler</code></a> during integration steps.</div> |
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| <td class="colFirst"><a href="../../../../../../org/apache/commons/math3/ode/events/EventHandler.Action.html" title="enum in org.apache.commons.math3.ode.events">EventHandler.Action</a></td> |
| <td class="colLast"> |
| <div class="block">Enumerate for actions to be performed when an event occurs.</div> |
| </td> |
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| <td class="colFirst"><a href="../../../../../../org/apache/commons/math3/ode/events/FilterType.html" title="enum in org.apache.commons.math3.ode.events">FilterType</a></td> |
| <td class="colLast"> |
| <div class="block">Enumerate for <a href="../../../../../../org/apache/commons/math3/ode/events/EventFilter.html" title="class in org.apache.commons.math3.ode.events"><code>filtering events</code></a>.</div> |
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| <h2 title="Package org.apache.commons.math3.ode.events Description">Package org.apache.commons.math3.ode.events Description</h2> |
| <div class="block"><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 <a href="../../../../../../org/apache/commons/math3/ode/events/EventHandler.html#g(double, double[])"><code>g(t, y)</code></a> |
| 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></div> |
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