Multiplying by the operator [ S ], the formula for the velocity v P takes the form: v P = [ Ω Ω ] ( P − − d ) + d ˙ ˙ = ω ω × × R P / O + v O , where the vector ω is the angular velocity vector obtained from the components of the matrix [Ω]; the vector R P / O = P − − d , is the position of P relative to the origin O of the moving frame M ; and v O = d ˙ ˙ , is the velocity of the origin O.