How to get angular momentum from two quaternions? - Java-Games

mayoneez wrote:

> I have a physics engine that I'm using in a simulation. As part of a
> Verlet intergration step, I need to be able to calculate the angular
> momentum for a rigid body, based on the start and end orientation of
> the body.
>
> This is what I know:
>
> q1 = start orientation of the body as a quaternion (which I can of
> course convert to a rotation matrix)
> q2 = end orientation of the body as a quaternion
> t = time elapsed between start and end orientation
> m = mass of the body
> I = inertia tensor of the body
>
> We can assume that angular velocity is constant during the
> rotation.
>
> How can I compute angular momentum of the body using the
> information listed above?

Angular momentum is L = I omega, where omega is the angular velocity of
the object and I is the moment of inertia (what I assume you mean by
inertia tensor above). That means

L = I dtheta/dt,

where theta is the angular displacement and t is time. So that's
approximately equal to

L = I delta theta/t

= I (theta_2 - theta_1)/t.

Where theta_1 is the initial angular displacement and theta_2 is the
final. So convert your starting and ending quaternions to angular
displacement vectors, divide by the elapsed time, and concatenate that
with your moment of inertia tensor. Convert between local and world
coordinates as necessary (you don't say which is in what coordinates above).

--
Erik Max Francis && max@alcyone.com && http://www.alcyone.com/max/
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-- Sandra St. Victor

Thanks. I'll give it a try.