Editing Verlet integration (section)

{{Short description|Numerical integration algorithm}}
'''Verlet integration''' ({{IPA|fr|vɛʁˈlɛ}}) is a numerical method used to [[Time integration method|integrate]] [[Isaac Newton|Newton's]] [[equations of motion]].<ref name="Verlet1967" /> It is frequently used to calculate [[Trajectory|trajectories]] of particles in [[molecular dynamics]] simulations and [[computer graphics]]. The algorithm was first used in 1791 by [[Jean Baptiste Joseph Delambre|Jean Baptiste 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 [[Philip Herbert Cowell|P. H. Cowell]] and [[Andrew Claude de la Cherois Crommelin|A. C. C. Crommelin]] in 1909 to compute the orbit of [[Halley's Comet]], and by [[Carl Størmer]] in 1907 to study the trajectories of electrical particles in a [[magnetic field]] (hence it is also called '''Størmer's method''').<ref>{{Cite book | last1=Press | first1=W. H. | last2=Teukolsky | first2=S. A. | last3=Vetterling | first3=W. T. | last4=Flannery | first4=B. P. | year=2007 | title=Numerical Recipes: The Art of Scientific Computing | edition=3rd | publisher=Cambridge University Press |  location=New York | isbn=978-0-521-88068-8 | chapter=Section 17.4. Second-Order Conservative Equations | chapter-url=http://apps.nrbook.com/empanel/index.html#pg=928}}
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The Verlet integrator provides good [[numerical stability]], as well as other properties that are important in [[physical system]]s such as [[time reversibility]] and [[Symplectic integrator|preservation of the symplectic form on phase space]], at no significant additional computational cost over the simple [[Euler method]].