Center of mass rigid body, the gravity forces will not cause the body to rotate, which means the weight of the body can be considered to be concentrated at the center of mass. The linear and angular momentum of a collection of particles can be simplified by measuring the position and velocity of the particles relative to the center of mass. Let the system of particles "P", "i"=1...,"n" of masses "m" be located at the coordinates r with velocities v. Select a reference point R and compute the relative position and velocity vectors, The total linear and angular momentum vectors relative to the
Cross product a and b provides an alternative definition of the cross product. The relation: can be compared with another relation involving the right-hand side, namely Lagrange's identity expressed as: where a and b may be "n"-dimensional vectors. This also shows that the Riemannian volume form for surfaces is exactly the surface element from vector calculus. In the case where , combining these two equations results in the expression for the magnitude of the cross product in terms of its components: The same result is found directly using the components of the cross product found from: In R, Lagrange's equation is a