Performance of implicit A-stable time integration methods for multibody system dynamics

This paper illustrates the performance of several representative implicit A-stable time integration methods with algorithmic dissipation for multibody system dynamics, formulated as a set of mixed implicit first-order differential and algebraic equations. The integrators include the linear multi-step methods with two to four steps, the single-step reformulations of the linear multi-step methods, and explicit first-stage, singly diagonally-implicit Runge–Kutta methods. All methods are implemented in the free, general-purpose multibody solver MBDyn. Their formulations and implementation are presented. According to the comparison from linear analysis and numerical experiments, some general conclusions on the selection of integration schemes and their implementation are obtained. Although all of these methods can predict reasonably accurate solutions, the specific advantages that each of them has in different situations are discussed.