Benchmarking of augmented Lagrangian and Hamiltonian formulations for multibody system dynamics

Augmented Lagrangian methods represent an efficient way to carry out the forward-dynamics simulation of mechanical systems. These algorithms introduce the constraint forces in the dynamic equations of the system through the use of a set of multipliers. While most of these formalisms were obtained using the system Lagrange's equations as starting point, a number of them have been derived from Hamilton's canonical equations. Besides being efficient, they are generally considered to be very robust, which makes them especially suitable for the simulation of systems with discontinuities and impacts. In this work, we have focused on the simulation of mechanical assemblies that undergo singular configurations. First, some sources of numerical difficulties in the proximity of singular configurations were identified and discussed. Afterwards, several augmented Lagrangian and Hamiltonian formulations were compared in terms of their robustness during the forward-dynamics simulation of two benchmark problems. The effect of the formulation and numerical integrator choice and parameters on the simulation performance was also assessed.status: accepte