On the design of energy preserving and decaying schemes for flexible, nonlinear multi-body systems

Energy preserving schemes achieve unconditional stability for nonlinear systems by establishing discrete energy preservation statements. Several schemes have been presented by various authors within drastically different frameworks: finite difference schemes based on a mid-point approximation, Galerkin and time discontinuous Galerkin approximations of the equations of motion written in the symmetric hyperbolic form, finite elements in time, and 2-stage FSAL Runge-Kutta methods. Furthermore, different types of parameterization of finite rotations were used in the various formulations. This paper presents a unified, finite difference framework which readily allows comparing the various schemes and their respective properties. Numerical examples are presented and show that the predictions of two of these schemes are in very close agreement with each other.