Velocity Verlet algorithm: Difference between revisions
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:<math>v \left(t+ \delta t\right) = v(t) + \frac{1}{2} \delta t [ a(t) + a(t+\delta t)]</math> | :<math>v \left(t+ \delta t\right) = v(t) + \frac{1}{2} \delta t [ a(t) + a(t+\delta t)]</math> | ||
where <math>r</math> is the position, <math>v</math> is the velocity and <math>t</math> is the time. | where <math>r</math> is the position, <math>v</math> is the velocity, <math>a</math> is the acceleration and <math>t</math> is the time. | ||
==See also== | ==See also== | ||
*[[Verlet leap-frog algorithm]] | *[[Verlet leap-frog algorithm]] | ||
Revision as of 09:00, 26 November 2010
The Velocity Verlet algorithm for use in molecular dynamics is given by
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r(t + \delta t) = r (t) + \delta t v(t) + \frac{1}{2} \delta t^2 a(t)}
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle v \left(t+ \delta t\right) = v(t) + \frac{1}{2} \delta t [ a(t) + a(t+\delta t)]}
where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r} is the position, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle v} is the velocity, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a} is the acceleration and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t} is the time.
See also
References
- Loup Verlet "Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules", Physical Review 159 pp. 98-103 (1967)
- William C. Swope, Hans C. Andersen, Peter H. Berens and Kent R. Wilson "A computer simulation method for the calculation of equilibrium constants for the formation of physical clusters of molecules: Application to small water clusters", Journal of Chemical Physics 76 pp. 637-649 (1982)
External resources
- Velocity version of Verlet algorithm sample FORTRAN computer code from the book M. P. Allen and D. J. Tildesley "Computer Simulation of Liquids", Oxford University Press (1989).