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Velocity Verlet Integration

  1. Dec 1, 2006 #1
    Hi!
    Could anyone explain me why Velocity Verlet integration works and how did Loup Verlet come up with it?

    Thanks!
     
  2. jcsd
  3. Dec 1, 2006 #2

    HallsofIvy

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  4. Dec 1, 2006 #3

    D H

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    I saw that too. Links from that page suggest that "Velocity Verlet" integration is somewhat different from "Verlet integration".

    EDIT

    Found it "http://www.ch.embnet.org/MD_tutorial/pages/MD.Part1.html" [Broken]. Velocity Verlet integration integrates velocity as well as position via a modified Euler scheme:
    [tex]v(t+\Delta t) = v(t) + \frac 1 2 (a(t)+a(t+\Delta t))\Delta t[/tex]

    Plain Jane Verlet integration computes velocity post-integration, resulting in [tex]O(\Delta t^2)[/tex] velocity errors. The Velocity Verlet integration yields [tex]O(\Delta t^3)[/tex] accuracy for velocity.

    /EDIT

    We typically use higher-order propagation techniques to achieve a high level of accuracy. It's pretty hard to beat good old RK4 in a regime where the integration frequency has to match the thruster control frequency (10 to 100 Hz or so) while the orbital dynamics operate at a much slower frequency.

    However, we sometimes need to revert to lower order techniques to model flex (very fast dynamics). This technique and related ones (e.g., "http://en.wikipedia.org/wiki/Beeman%27s_algorithm" [Broken]) look very promising.

    Thanks to the OP.
     
    Last edited by a moderator: Apr 22, 2017 at 2:22 PM
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