GAUSS PRINCIPLE OF LEAST CONSTRAINT IN GENERALIZED COORDINATES AND ITS GENERALIZATION

When the generalized coordinates are used to describe the motion of a system, a higher computational efficiency will be achieved in using the Gauss principle of least constraint, as compared with in the form of mass points. Based on the Gauss principle in the form of variation, the Gauss principle of least constraint in generalized coordinates is derived. The principle is generalized to cases of non-ideal constraints, unilateral constraints and the collision of rigid body systems. For the collision problem of rigid body systems, it is shown that the collision law cannot be replaced by the Gauss principle of least constraint and it should be used in the form of constraint equations for generalized velocities after collision.