Group theory in the problems of modeling and control of multi-body systems. (English) Zbl 1121.70007

Summary: This work is a review of our research activity during the last ten years concerning the modeling and control of multi-body mechanical systems. Because the treatment of the above topics is quite sensitive to different parameterizations of the rotation group in three-dimensional space SO(3) and because the properties of the parameterization more or less influence the efficiency of the dynamic model, here the so-called vector-parameter is used for parallel considerations. The consideration of the mechanical system in the configurational space of pure vector-parameters with a group structure opens the possibilities for Lie group theory to be applied to the problems of dynamics and control. The sections in this paper an independent parts of a unified approach.


70E55 Dynamics of multibody systems
70Q05 Control of mechanical systems
70-02 Research exposition (monographs, survey articles) pertaining to mechanics of particles and systems
22E70 Applications of Lie groups to the sciences; explicit representations