An Implicit Runge–Kutta Method for Integration of Differential Algebraic Equations of Multibody Dynamics

When performing dynamic analysis of a constrained mechanical system, aset of index 3 Differential Algebraic Equations (DAE) describes the timeevolution of the model. This paper presents a state space DAE solutionframework that can embed an arbitrary implicit Ordinary DifferentialEquations (ODE) code for numerical integration of a reduced set of statespace ordinary differential equations. This solution framework isconstructed with the goal of leveraging with minimal effort establishedoff the shelf implicit ODE integrators for efficiently solving the DAEof multibody dynamics. This concept is demonstrated by embedding awell-known public domain singly diagonal implicit Runge–Kutta code inthe framework provided. The resulting L-stable, stiffly accurateimplicit algorithm is shown to be two orders of magnitude faster than astate of the art explicit algorithm when used to simulate a stiffvehicle model.