The stability of exponential variational integrators as key role tool in studying multibody holonomic systems

The role of stability of high order exponential variational integrators (EVIs) when they are applied to mechanical systems with holonomic constraints, is extensively examined and discussed. This class of geometric type integration schemes are determined through a discretization of the variational Hamilton's principle and the definition of a characteristic discrete Lagrangian. The formulation of exponential interpolation functions is tested on the discrete Euler-Lagrangian equations in the presence of constraints. The resulting schemes are then applied on dynamical multibody systems with holonomic constraints, choosing the double pendulum as a concrete example. The long-time behavior of the EVIs, which reflects their property of stability was found to be very good compared to that of other traditional methods.