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Do Inertia Tensors change?

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AFAIK it won't change unless the distribution of mass changes. In other words, if you're using rigid-bodies then it won't change. If your objects deform, it *should* be recalculated, but unless the deformation is significant (and you're going for a very realistic simulation) then you could probably get away with leaving it as is.

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The inertia tensor of a rigid body is fixed in the local/body frame of reference, but changes as the body rotates in the global/world frame of reference.

Recalculating it is expensive so it's generally easisest to as much rotational dynamics as possible in the body frame of reference, only switching to a world frame of reference when necessary (e.g. to resolve collisions between bodies with different orientations and so different frames of reference).

Also the inertia tensor in a world frame of reference can be calulated from the body centred one using

I' = RIR-1

A calculation that's easier if I is a diagonal matrix (as it often is for symmertric bodies).

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