Posing Multibody Dynamics with Friction and Contact as a Differential Complementarity Problem

This technical brief revisits the method outlined in [1], which was introduced to solve the multibody dynamics problem in the presence of friction and contact. Instead of using maximum dissipation conditions as the basis for the Coulomb friction model, the approach detailed relies on complementarity conditions that combine with contact unilateral constraints to augment the classical index-3 differential algebraic equations of multibody dynamics. The resulting set of differential, algebraic and complementarity equations is relaxed after time discretization to a cone complementarity problem whose solution represents the first order optimality condition of a quadratic program with conic constraints. The differential complementarity approach discussed is versatile. It has been recently validated in the context of granular dynamics and used in fluid-solid interaction problems to model both the fluid and solid phases.