Mechanical systems subject to holonomic constraints: Differential–algebraic formulations and conservative integration

The numerical integration in time of the equations of motion for mechanical systems subject to holonomic constraints is considered. Schemes are introduced for the direct treatment of a differential–algebraic form of the equations that preserve the constraints, the total energy, and other integrals such as linear and angular momentum arising from affine symmetries. Moreover, the schemes can be shown to preserve the property of time-reversibility in an appropriate sense. An example is given to illustrate various aspects of the proposed methods. ©1999 Elsevier Science B.V. All rights reserved. PACS: 02.70.Ns; 02.60.Jh; 03.20.+i