A note on holonomic costraints

Abstract

We propose a new description of dynamics of autonomous mechanical systems which includes the momentum-velocity relation. This description is formulated as a variational principle of virtual action more complete than the Hamilton Principle. The inclusion of constraints in this description is the main topic of the present note. We give examples and models of constraints in variational formulations of statics and dynamics of autonomous systems. Holonomic constraints are usually interpreted as restrictions on configurations of a mechanical system. Nonholonomic constraints are additional restrictions imposed on velocities. This traditional terminology is not adapted to our concept of constraints as imposed on virtual displacements and only indirectly affecting configurations and velocities. Our concept of nonholonomic constraints makes perfect sense for static systems even if velocities do not appear in the description of such systems.