Exponential variational integrators for the dynamics of multibody systems with holonomic constraints

We here explore a geometric integrator scheme that is determined by a
discretization of a variational principle using a higher-order Lagrangian that uses exponential type of interpolation functions. The resulting exponential variational integrators are here extended to conservative mechanical systems with constraints. To do so we first present continuous Euler-Lagrangian equations with holonomic constraints and then mimic the process
for the discrete case. The resulting schemes are then tested to a typical dynamical multibody system with constraints, i.e the double pendulum showing the good long-time behavior when compared to other traditional methods.