Rigid body dynamics The result is a set of m equations of motion that define the dynamics of the rigid body system. If the generalized forces Q are derivable from a potential energy V(q...,q), then these equations of motion take the form In this case, introduce the Lagrangian, L=T-V, so these equations of motion become These are known as Lagrange's equations of motion. The linear and angular momentum of a rigid system of particles is formulated by measuring the position and velocity of the particles relative to the center of mass. Let the system of particles P, i=1...,n be located at the coordinates
Linear motion According to Newton's first law of motion, objects that do not experience any net force will continue to move in a straight line with a constant velocity until they are subjected to a net force. Under everyday circumstances, external forces such as gravity and friction can cause an object to change the direction of its motion, so that its motion cannot be described as linear. One may compare linear motion to general motion. In general motion, a particle's position and velocity are described by vectors, which have a magnitude and direction. In linear motion, the directions of all the vectors