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inertia tensor

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i am looking for a little help or maybe a more clear explanation about the inertia tensor. i am doing a simulation with some cubes and i fully understand how the moment of inertia about each axis is calculated and such. however i am confused with the tensor. what i think i understand is that i do not necessarily need the tensor represented as a 3 by 3 matrix to correctly represent the moment of inertia if my rigid body is completley symmetrical about each axis of rotation. like my cube, or a sphere or a rectangle. if the body is completely symmetrical about each axis in local or object space than i can represent its moment of inertia in my simulation as simply a vector, or in this case as a simple scalar actually since for the cube this value would be the same for each component (x,y,z). is this correct then??

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No, because you have to do a matrix multiply with the inertia tensor, when you''re doing the similarity transform (R * Ib * R''). R being the orientation, Ib inertia tensor in body coordinates, and R'' is the transpose of the orientation. You could store Ib as a vector and write a special multiply routine for it.

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the vector would represent the diagonal of the matrix, but you''d be better off using a matrix straight away. The inertia tensor would be a diagonal matrix in object space, but not in world space.

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