|Dec1-06, 08:19 AM||#1|
Velocity Verlet Integration
Could anyone explain me why Velocity Verlet integration works and how did Loup Verlet come up with it?
|Dec1-06, 10:12 AM||#2|
I had never heard of "Vertlet integration" before I saw this!
|Dec1-06, 10:52 AM||#3|
I saw that too. Links from that page suggest that "Velocity Verlet" integration is somewhat different from "Verlet integration".
Found it here. 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.
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.
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