Spacetime as a redshift and analyze the effect in terms of scenarios (b) or (d). In classical mechanics, the state of motion of a particle is characterized by its mass and its velocity. Linear momentum, the product of a particle's mass and velocity, is a vector quantity, possessing the same direction as the velocity: p = "mv". It is a "conserved" quantity, meaning that if a closed system is not affected by external forces, its total linear momentum cannot change. In relativistic mechanics, the momentum vector is extended to four dimensions. Added to the momentum vector is a time component that
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