I ran into the following problem, and stuck for a couple of days now. I have a solid body, rigid and and has uniform density. Its mass M, the location of the center of gravity x_M, y_M, z_M and its inertia matrix is known: Jx Jxy Jxz Jyx Jyy Jyz Jzx Jzy Jz I have to write an algorithm, which creates maximum 3 mass points xi, yi, zi, mi in a way, that the following properties of the solid body and the sum of the mass points are exactly the same: - The mass must be identical ∑i=13mi = M - The location of the center of gravity must remain xM =∑i=13mi xi/M yM =∑i=13mi yi/M zM =∑i=13mi zi/M - Jx must be unchanged: JxM = ∑i=13 (yi2 + zi2) mi - The angle of the principal axes to x axis should not change JxyM = ∑i=13 xiyimi JxzM = ∑i=13 xizimi Everything else is arbitrary. What I did so far: with simple algebra I managed to find a solution for everything, except for Jxy and Jxz. But I see no way to modify the variables to keep the good parameters and reach the missing ones at the same time. Any suggestions are most welcome, many thanks in advance.