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inertia vector and inverse inertia vector

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If I define an inertia vector of a body, which is the diagonal of the inertia tensor, then can I get the global inertia with quaternions too? Like: I = o * Ibody * ~o o is the orientation quat., ~o is the conjugate of o. How can I then calculate the inverse of I (each element''s invers) without dividing every frame? I want to store the Ibody''s inverse like inverse Ibody tensors.

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