Difference between revisions of "Verlet integration"
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| − | '''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. | It is frequently used to calculate trajectories of particles in molecular dynamics simulations and computer graphics. | ||
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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. | 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. | 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. | ||
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* [[Algorithm]] | * [[Algorithm]] | ||
| − | * [[Euler | + | * [[Euler method]] |
| + | * [[Numerical analysis]] | ||
== External links == | == External links == | ||
* [https://en.wikipedia.org/wiki/Verlet_integration Verlet integration] | * [https://en.wikipedia.org/wiki/Verlet_integration Verlet integration] | ||
Revision as of 14:19, 13 August 2015
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.
