> Similar formulas exist for moments, to compute the inertia matrix for a rigid body.
Fun fact. The inertia for any rigid body can be represented by 4 point masses forming a tetrahedron. If you diagonalize the inertia matrix, the coordinates of the 4 point masses can be (x, y, -z) (-x,-y,-z) (x, -y, z) (-x, y, z) where x,y,z are easy to calculate (I wrote this all down ages ago). You can also represent any point on the rigid body by its barycentric coordinates relative to those points. I believe an impulse can be applied, by finding the barycentric coordinates of the point its applied and using those coordinates to distribute the impulse to the 4 masses.
This is all really cool with one huge exception. The 4 points become coplanar for large flat objects, which means the z-height is really small for a piece of sheet metal for example.
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Fun fact. The inertia for any rigid body can be represented by 4 point masses forming a tetrahedron. If you diagonalize the inertia matrix, the coordinates of the 4 point masses can be (x, y, -z) (-x,-y,-z) (x, -y, z) (-x, y, z) where x,y,z are easy to calculate (I wrote this all down ages ago). You can also represent any point on the rigid body by its barycentric coordinates relative to those points. I believe an impulse can be applied, by finding the barycentric coordinates of the point its applied and using those coordinates to distribute the impulse to the 4 masses.
This is all really cool with one huge exception. The 4 points become coplanar for large flat objects, which means the z-height is really small for a piece of sheet metal for example.