Momentum motion. The first use of "momentum" in its proper mathematical sense is not clear but by the time of Jenning's "Miscellanea" in 1721, five years before the final edition of Newton's "Principia Mathematica", momentum or "quantity of motion" was being defined for students as "a rectangle", the product of and , where is "quantity of material" and is "velocity", . Momentum In Newtonian mechanics, linear momentum, translational momentum, or simply momentum (pl. momenta) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction in three-dimensional space. If is
Rigid body dynamics the rigid body. The velocity of the points R along their trajectories are where ω is the angular velocity vector of the body. Work is computed from the dot product of each force with the displacement of its point of contact If the trajectory of a rigid body is defined by a set of generalized coordinates "q", "j" = 1, ..., "m", then the virtual displacements δr are given by The virtual work of this system of forces acting on the body in terms of the generalized coordinates becomes or collecting the coefficients of δq For simplicity consider a trajectory