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http://crossmark.crossref.org/dialog/?doi=10.1007/s00707-016-1760-9&domain=pdf
Web End = Acta Mech 227, 33273350 (2016)
DOI 10.1007/s00707-016-1760-9
REVIEW AND PERSPECTIVE IN MECHANICS
Received: 11 October 2016 / Revised: 29 October 2016 / Published online: 1 December 2016 The Author(s) 2016. This article is published with open access at Springerlink.com
Abstract Multibody systems are dynamical systems characterized by intrinsic symmetries and invariants. Geometric mechanics deals with the mathematical modeling of such systems and has proven to be a valuable tool providing insights into the dynamics of mechanical systems, from a theoretical as well as from a computational point of view. Modeling multibody systems, comprising rigid and exible members, as dynamical systems on manifolds, and Lie groups in particular, leads to frame-invariant and computationally advantageous formulations. In the last decade, such formulations and corresponding algorithms are becoming increasingly used in various areas of computational dynamics providing the conceptual and computational framework for multibody, coupled, and multiphysics systems, and their nonlinear control. The geometric setting, furthermore, gives rise to geometric numerical integration schemes that are designed to preserve the intrinsic structure and invariants of dynamical systems. These naturally avoid the long-standing problem of parameterization singularities and also deliver the necessary accuracy as well as a long-term stability of numerical solutions. The current intensive research in these areas documents the relevance and potential for geometric methods in general and in particular for multibody system dynamics. This paper provides an exhaustive summary of the development in the last decade, and a panoramic overview of the current state of knowledge in the eld.
1 Introduction
Space kinematics is solely based on screw theory, and consequently so is the kinematics of multibody systems (MBS). Even though such concepts are not so widely known in the MBS community, which is an obstacle hindering a fruitful exploitation of such concepts for computational MBS dynamics. On the other hand, a recent trend in MBS dynamics is to employ the terminology and certain concepts of Lie groups noting that rigid body motions, i.e., nite frame transformations, form such a group possessing certain desirable properties. The link between the theory of screws and motion groups is the fact that the screw algebra is nothing but the Lie algebra of the Lie group in question. The aim of this review paper is to discuss...