A Study on Mixed Kinetic-Kinematic Equations for Multibody Systems

Abstract

In this paper, mixed kinetic-kinematic equations for a multibody system have been studied in order to resolve the difficulties of non-integrability of angular velocity vectors. As for the kinetic equations, the Newton-Euler equations of motion are considered. They are derived in terms of angular velocity and angular acceleration vectors expressed in the body fixed reference frames. As for the kinematic compatibility equations, two different equations are considered. One is from the relationship between the angular velocity vector and the time derivatives of Euler parameters. The other is from the relationship between the rotational orientation matrix, its time derivative, and the angular velocity vector. In order to investigate the accuracy of the solution methods using two different kinematic compatibility equations, simulations of a spherical pendulum model and a 1/6 robot vehicle model have been carried out. With different integration step-sizes, the constraint violation errors have been also investigated.