same as the initial volume. Consider an inertial frame ( X 1 , X 2 , X 3 ) and a rotating frame ( x 1 , x 2 , x 3 ) , with L ( t ) being the linear transformation such that x = L X and it is clear that L is orthogonal, i.e., L L T = L T L = I . We can define an anti-symmetric matrix with this,