where we used eq 8 and UU T = I. We conclude that 4D rotations by U correspond to the required equimomental transformations. However, to interpret the 4D-rotated vectors s i = DUq i in terms of point masses in 3D, care must be taken to adjust also the masses m i by mutiplying them with the square of the fourth element of the rotated 4-vector, m i = m i (s i,4 ) 2 . This ensures that r i ≡ s i /s i,4 = r i,x , r i,y , r i,z , 1 T defines transformed 3D positions r i,x , r i,y , r i,z T with transformed masses m i that together leave X and thus the inertia tensor, center of mass, and total mass unchanged. Importantly, the resulting masses are bounded by 0