The formula for the acceleration A P can now be obtained as: A P = Ω Ω ˙ ˙ ( P − − d ) + A O + Ω Ω 2 ( P − − d ) , or A P = α α × × R P / O + ω ω × × ω ω × × R P / O + A O , where α is the angular acceleration vector obtained from the derivative of the angular velocity matrix; R P / O = P − − d , is the relative position vector (the position of P relative to the origin O of the moving frame M); and A O = d ¨ ¨ is the acceleration of the origin of the moving frame M.