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Dirk Gregorius

Integrating angular velocity ( Corioles term )

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The Newton-Euler equations in a rigid body simualtion have the following form: M * dv/dt = f_ext I * dw/dt = t_ext - [w]* I * w The term [w] * I * w is sometimes called Corioles term in the literature. IIRC this term is responsible for making a simple semi-implicit Euler instable - especially for long and thin objects and larger time-steps. 1) How can I compute an estimation of the max timestep I can take given the local intertia tensor of an object? 2) Can I invert this and compute a max ratio of the min element to the max element of the inertia tensor in order to detect critical objects? Are there any rules of thumb? 3) What would be a good rescue operation after accidently making a critical timestep for such an object? 4) Are there any other factors I need t take into account and that I overlooked here when dealing with long and thin objects in a velocity constraint LCP simulator? These critical objects (long and thin) are normaly not part of an articulation, so I am looking for some kind of heuristic to deal with them. I added some kind of clamping, where I define the minimum of an element of inertia tensor to be at least some amount (e.g. 5%) of the maximum element. You can't get save here without making the simulation unrealistic. Another solution would be to clamp the applied torque before integration, but which upper bound should I chose. I am bound to a semi-implicit Euler because of the velocity constraint LCP formulation I use, so I can't use Verlet, RK4 or implicit Euler which might help here... Any help is greatly appreciated! Regards, -Dirk

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