Verlet integration - Revision history

Karl Jones at 22:29, 20 April 2016

2016-04-20T22:29:44Z

Karl Jones at 10:15, 7 February 2016

2016-02-07T10:15:44Z

Karl Jones: equations of motion

2015-08-13T21:20:04Z

equations of motion

Karl Jones: etc

2015-08-13T21:19:28Z

etc

Karl Jones: First

2015-08-13T21:11:48Z

First

New page

'''Verlet integration''' (French pronunciation: [vɛʁˈlɛ]) is a numerical method used to integrate Newton's equations of motion.

It is frequently used to calculate trajectories of particles in molecular dynamics simulations and computer graphics.

The algorithm was first used in 1791 by Delambre, and has been rediscovered many times since then, most recently by Loup Verlet in the 1960s for use in molecular dynamics.

It was also used by Cowell and Crommelin in 1909 to compute the orbit of Halley's Comet, and by Carl Størmer in 1907 to study the motion of electrical particles in a magnetic field.

The Verlet integrator provides good numerical stability, as well as other properties that are important in physical systems such as time-reversibility and preservation of the symplectic form on phase space, at no significant additional computational cost over the simple Euler method.

Verlet integration was used by Carl Størmer to compute the trajectories of particles moving in a magnetic field (hence it is also called Störmer's method) and was popularized in molecular dynamics by French physicist Loup Verlet in 1967.

== See also ==

* [[Algorithm]]
* [[Euler integration]]

== External links ==

* [https://en.wikipedia.org/wiki/Verlet_integration Verlet integration]

← Older revision		Revision as of 22:29, 20 April 2016
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	* [https://en.wikipedia.org/wiki/Verlet_integration Verlet integration]		* [https://en.wikipedia.org/wiki/Verlet_integration Verlet integration]
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		+	[[Category:Algorithms]]
		+	[[Category:Mathematics]]
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 '''Verlet integration''' (French pronunciation: [vɛʁˈlɛ]) is a [[Numerical analysis|numerical method]] used to integrate Newton's [[equations of motion]].
 It is frequently used to calculate trajectories of particles in molecular dynamics simulations and computer graphics.
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 * [[Equations of motion]]
 * [[Euler method]]
 * [[Numerical analysis]]

@@ Line 1: / Line 1: @@
-'''Verlet integration''' (French pronunciation: [vɛʁˈlɛ]) is a [[Numerical analysis|numerical method]] used to integrate Newton's equations of motion.
+'''Verlet integration''' (French pronunciation: [vɛʁˈlɛ]) is a [[Numerical analysis|numerical method]] used to integrate Newton's [[equations of motion]].
 It is frequently used to calculate trajectories of particles in molecular dynamics simulations and computer graphics.
@@ Line 14: / Line 14: @@
 * [[Algorithm]]
 * [[Euler method]]
 * [[Numerical analysis]]

@@ Line 1: / Line 1: @@
-'''Verlet integration''' (French pronunciation: [vɛʁˈlɛ]) is a numerical method used to integrate Newton's equations of motion.
+'''Verlet integration''' (French pronunciation: [vɛʁˈlɛ]) is a [[Numerical analysis|numerical method]] used to integrate Newton's equations of motion.
 It is frequently used to calculate trajectories of particles in molecular dynamics simulations and computer graphics.
@@ Line 7: / Line 7: @@
 It was also used by Cowell and Crommelin in 1909 to compute the orbit of Halley's Comet, and by Carl Størmer in 1907 to study the motion of electrical particles in a magnetic field.
-The Verlet integrator provides good numerical stability, as well as other properties that are important in physical systems such as time-reversibility and preservation of the symplectic form on phase space, at no significant additional computational cost over the simple Euler method.
+The Verlet integrator provides good numerical stability, as well as other properties that are important in physical systems such as time-reversibility and preservation of the symplectic form on phase space, at no significant additional computational cost over the simple [[Euler method]].
 Verlet integration was used by Carl Størmer to compute the trajectories of particles moving in a magnetic field (hence it is also called Störmer's method) and was popularized in molecular dynamics by French physicist Loup Verlet in 1967.
@@ Line 14: / Line 14: @@
 * [[Algorithm]]
-* [[Euler integration]]
+* [[Euler method]]
 == External links ==
 * [https://en.wikipedia.org/wiki/Verlet_integration Verlet integration]