Multibody Systems

Abstract

A multibody system consists of rigid bodies between which act internal forces and torques that originate from massless constraint and coupling elements. In addition, other arbitrary external forces and torques can also influence the system. A mass point system is a special case of a multibody system. For example, we can represent a multibody system as a mass point system if all rotational velocities and all internal and external torques vanish with respect to the body center of mass. In comparison to a free multibody system, a free mass point system has only half the number of degrees of freedom because of the omitted rotations. In the case of a planar multibody system, one displacement coordinate and two angular coordinates are dropped as well as one force coordinate and two torque coordinates. Moreover, all bodies must move in parallel principal planes of inertia. In comparison to a free, three-dimensional multibody system, the number of degrees of freedom in a free planar multibody system is reduced by half. Similar simplifications result in gyroscopic systems or planar point systems. In order to limit the diversity of variants, we will only discuss the three-dimensional multibody system. The simplifications in the aforementioned special cases, which lead to a complete cancelation of vanishing equations, will be left to the reader, though they will to some extent be encountered in the examples.