The acceleration of P (t) in F is obtained as the time derivative of the velocity, A P = P ¨ ¨ ( t ) = [ Ω Ω ˙ ˙ ] P + [ Ω Ω ] P ˙ ˙ , which becomes A P = [ Ω Ω ˙ ˙ ] P + [ Ω Ω ] [ Ω Ω ] P , where [ Ω Ω ˙ ˙ ] = [ 0 − − α α α α 0 ] , is the angular acceleration matrix of M on F, and α α = d 2 θ θ d t 2 .