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Mathematical Problems in Engineering
Volume 8 (2002), Issue 3, Pages 169-180

On potential energies and constraints in the dynamics of rigid bodies and particles

1Department of Mechanical Engineering, University of California at Berkeley, Berkeley, California 94720-1740, USA
2Department of Mechanical Engineering, Texas A&M University, College Station, Texas 77843-3123, USA

Received 2 October 2001

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A new treatment of kinematical constraints and potential energies arising in the dynamics of systems of rigid bodies and particles is presented which is suited to Newtonian and Lagrangian formulations. Its novel feature is the imposing of invariance requirements on the constraint functions and potential energy functions. These requirements are extensively used in continuum mechanics and, in the present context, one finds certain generalizations of Newton's third law of motion and an elucidation of the nature of constraint forces and moments. One motivation for such a treatment can be found by considering approaches where invariance requirements are ignored. In contrast to the treatment presented in this paper, it is shown that this may lead to a difficulty in formulating the equations governing the motion of the system.