On the Numerical Solution of Euler-Lagrange Equations∗

The Euler-Lagrange equations that describe the motion of constrained mechanical systems are locally reduced to a system of ordinary differential equations by means of local parametrizations. The class of local pa-rametrizations considered contains as particular cases the tangent plane parametrization and the local parametrization that is induced by the method of generalized coordinate partitioning. Explicit and implicit multi-step algorithms are developed in this framework. A numerical example shows that explicit methods may fail, while implicit methods are successful.