# Velocity Verlet Integration

1. Dec 1, 2006

### squid

Hi!
Could anyone explain me why Velocity Verlet integration works and how did Loup Verlet come up with it?

Thanks!

2. Dec 1, 2006

### HallsofIvy

Staff Emeritus
3. Dec 1, 2006

### D H

Staff Emeritus
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". Velocity Verlet integration integrates velocity as well as position via a modified Euler scheme:
$$v(t+\Delta t) = v(t) + \frac 1 2 (a(t)+a(t+\Delta t))\Delta t$$

Plain Jane Verlet integration computes velocity post-integration, resulting in $$O(\Delta t^2)$$ velocity errors. The Velocity Verlet integration yields $$O(\Delta t^3)$$ 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: May 2, 2017