This paper describes two aspects of multibody system (MBS) dynamics on a generalized mass metric in Riemannian velocity space and recursive momentum formulation. Firstly, we present a detailed expression of the Riemannian metric and operator factorization of a generalized mass tensor for the dynamics of general-topology rigid MBS. The derived expression allows a clearly understanding the components of the generalized mass tensor, which also constitute a metric of the Riemannian velocity space. It is being the fact that there does exist a common metric in Lagrange and recursive Newton-Euler dynamic equation, we can determine, from the Riemannian geometric point of view, that there is the equivalent relationship between the two approaches to a given MBS. Next, from the generalized momentum definition in the derivation of the Riemannian velocity metrics, recursive momentum equations of MBS dynamics are developed for progressively more complex systems: serial chains, topological trees, and closed-loop systems. Through the principle of impulse and momentum, a new method is proposed for reorienting and locating the MBS form a given initial orientation and location to desired final ones without needing to solve the motion equations.
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ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
September 4–7, 2007
Las Vegas, Nevada, USA
Conference Sponsors:
- Design Engineering Division and Computers and Information in Engineering Division
ISBN:
0-7918-4806-X
PROCEEDINGS PAPER
Dynamics of Multibody Systems: Generalized Mass Metric in Riemannian Velocity Space and Recursive Momentum Formulation
Qiang Zhao,
Qiang Zhao
Ecole de Technologie Supe´rieure Universite´ du Quebec, Montre´al, QC, Canada
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Hong Tao Wu
Hong Tao Wu
Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu, China
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Qiang Zhao
Ecole de Technologie Supe´rieure Universite´ du Quebec, Montre´al, QC, Canada
Hong Tao Wu
Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu, China
Paper No:
DETC2007-34657, pp. 633-641; 9 pages
Published Online:
May 20, 2009
Citation
Zhao, Q, & Wu, HT. "Dynamics of Multibody Systems: Generalized Mass Metric in Riemannian Velocity Space and Recursive Momentum Formulation." Proceedings of the ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 5: 6th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C. Las Vegas, Nevada, USA. September 4–7, 2007. pp. 633-641. ASME. https://doi.org/10.1115/DETC2007-34657
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