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I've decided that I don't need a huge amount of accuracy in the final simulation, so I was hoping to represent any rotating object as an aggregation of several smaller, simpler objects. For example, a rotating ice cream cone I could fudge as a cone and a sphere. With this method, I was hoping to get around a lot of slow and complex mathematics.

Here was my idea: If I know the inertia tensors for simple objects like spheres and rods around their primary axes, I can just shift my moments and sum them up into a final tensor, eliminating the need to transform coordinates and find eigenvalues.

For example: if I had an object that was composed of a solid sphere and a solid circular cylinder, with the center of mass of the sphere 5 units to the left of the object, and the CoM of the cylinder 2 units down from the CoM of the object, I could say that

(sphere)

Ixx = 2/5mr^2 + 25m

All other moments stay as they were; the products of inertia still remain zero.

(cylinder)

Izz = 1/2mr^2 + 4m

All other moments stay as they were; the products of inertia still remain zero.

Then I could take these two inertia tensors and add them together to get the final tensor of my aggregate object.

Will this work? Can I do the parallel axis shifts like that in 3D?

Thanks in advance!