Nonholonomic multibody dynamics

The paper deals with the nonholonomic multibody system dynamics from a point of view which is caused by some actual applications in high-tec areas like high-speed train technology or biomechanics of some disciplines in high-performance sports. Obviously, looking at such problems, there are very close connections between classical analytical dynamics, differential geometry and modern control theory. But these connections cannot be used to get new composed results in solving complicated problems of multibody system dynamics because corresponding software tools are not enough in tune with each other. This paper will give some ideas for developing a unified basis for modeling, simulation and control of nonholonomic multibody systems. First, a derivative-free approach for generating Lagrangian motion equations of multibody systems with kinematical tree structure as well as for constrained multibody systems is given. This has been done by using differential-geometric concepts in a Riemannian space. Secondly, the well-known theorem of Frobenius is considered with respect to its classical interpretation by the so-called object of nonholonomy as well as by its modern interpretation in the nonlinear control theory using Lie-brackets. The ideas are illustrated by the classical rolling condition and edge condition on double-curved surfaces. Special numerical problems in simulation of multibody systems subject to additional kinematic constraints are discussed. Finally three applications are given.