On the stability of exponential variational integrators for multibody systems with holonomic constraints

In the present we test the stability of the high order exponential variational integrators when applied to mechanical systems with holonomic constraints. Those geometric integrator schemes are determined by a discretization of a variational principle for a discrete Lagrangian. That expression, which is defined using exponential expressions of interpolation functions, is then applied on the discrete Euler-Lagrangian equations with constraints. The resulting schemes are then tested on a typical dynamical multibody system with constraints, i.e the double pendulum, and show good long-time behavior when compared to other traditional methods. (paper)