Implicit Runge-Kutta Integration of the Equations of Multibody Dynamics in Descriptor Form

ABSTRACT

Implicit Runge-Kutta integration algorithms based on generalized coordinate partitioning are presented for numerical solution of the differential-algebraic equations of motion of multibody dynamics. Second order integration formulas are derived from well known first order Runge-Kutta integrators, defining independent generalized coordinates and their first time derivative as functions of independent accelerations. The latter are determined as the solution of discretized equations of motion that are obtained by inflating underlying state space, second order ordinary differential equations of motion in independent coordinates to descriptor form. Dependent variables in the formulation, including Lagrange multipliers, are determined using kinematic and kinetic equations of multibody dynamics. The proposed method is tested with a large-scale mechanical system that exhibits stiff behavior. Results show that the algorithm is robust and has the capability to integrate the differential-algebraic equations of motion for stiff multibody dynamic systems.