Generalized Coordinates

Abstract

In many cases, the motion of bodies considered in mechanics is not free but is restricted by certain constraint conditions. The constraints can take different forms. For instance, a mass point can be bound to a space curve or to a surface. The constraints for a rigid body state that the distances between the individual points are constant. If one considers gas molecules in a vessel, the constraints specify that the molecules cannot penetrate the wall of the vessel. Since the constraints are important for solving a mechanical problem, mechanical systems are classified according to the type of constraints. Taking into account these constraints, a mechanical system often can be described by a new set of coordinates, the so-called generalized coordinates.