How does Velocity Verlet integration improve accuracy in modeling fast dynamics?

[squid]

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

Thanks!

 

[HallsofIvy]

I had never heard of "Vertlet integration" before I saw this!

Try here:
http://en.wikipedia.org/wiki/Verlet_integration

 

[D H]

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" ) look very promising.

Thanks to the OP.