An implicit Runge-Kutta method for integration of differential algebraic equations of multibody dynamics

When performing dynamic analysis of a constrained mechanical system, a set of index 3 Differential Algebraic Equations (DAE) describes the time evolution of the model. This paper presents a state space DAE solution framework that can embed an arbitrary implicit Ordinary Differential Equations (ODE) code for numerical integration of a reduced set of state space ordinary differential equations. This solution framework is constructed with the goal of leveraging with minimal effort established off the shelf implicit ODE integrators for efficiently solving the DAE of multibody dynamics. This concept is demonstrated by embedding a well-known public domain singly diagonal implicit Runge-Kutta code in the framework provided. The resulting L-stable, stiffly accurate implicit algorithm is shown to be two orders of magnitude faster than a state of the art explicit algorithm when used to simulate a stiff vehicle model.