Geometric methods and formulations in computational multibody system dynamics

Mueller, Andreas and Terze, Zdravko (2016) Geometric methods and formulations in computational multibody system dynamics. = Geometric methods and formulations in computational multibody system dynamics. Acta mechanica, 227 (12). pp. 3327-3350. ISSN 0001-5970. Vrsta rada: ["eprint_fieldopt_article_type_article" not defined]. Kvartili JCR: Q2 (2016). Točan broj autora: 2.

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Official URL: https://link.springer.com/article/10.1007/s00707-0...

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 flexible 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 field.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 flexible 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 field.

Item Type: Article (["eprint_fieldopt_article_type_article" not defined])
Keywords (Croatian): constraint violation ; Lagrange equations ; lie groups Multibody systems ; numerical integration
Subjects: NATURAL SCIENCES > Mathematics
Divisions: 1300 Department of Aeronautical Engineering > 1320 Chair of Aircraft Dynamics
Indexed in Web of Science: Yes
Indexed in Current Contents: Yes
Citations JCR: 0 (10.01.2018.)
Quartiles: Q2 (2016)
Date Deposited: 10 Jan 2018 13:20
Last Modified: 10 Jan 2018 13:47
URI: http://repozitorij.fsb.hr/id/eprint/8215

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