A comparison of one-step methods for multibody system dynamics in descriptor and state space form

Abstract For an insulator chain and a multiple pendulum the equations of motion are given in descriptor form as differential-algebraic equations (DAEs) of index 2 and in state space form as ordinary differential equations (ODEs). The performance of two recently developed codes for the numerical solution of DAEs of index 2, the extrapolation code MEXX and the Runge-Kutta code HEM5, are compared with classical ODE-codes. Although the dimension of the DAEs in descriptor form is much larger than the dimension of the ODEs in state space form, the computing times are comparable if the sparse structure of the DAEs is exploited. The DAE-codes are as reliable as the ODE-codes. Therefore, the use of the DAE-codes is recommended for the simulation of constrained mechanical systems with tree structure or few closed loops, since the generation of the equations of motion in descriptor form is much easier.