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Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain


Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email:

Formulation of the Governing Equations of Motion of Dynamic Systems on a Principal Bundle

Journal of Applied Nonlinear Dynamics 9(1) (2020) 129--152 | DOI:10.5890/JAND.2020.03.011

Xiaobo Liu

General Motors Company, 800 North Glenwood Ave., Pontiac, MI 48340, USA

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In this paper, we present a geometric approach to form the governing equations of motion of dynamic systems. A geometric form of the d’Alembert-Lagrange equation on the configuration manifold is first developed and extended to a principal bundle. We can then obtain the explicit form of equations of motion by explicating the geometric form in a coordinate neighborhood on the principal bundle. This approach conveniently permits the choice of quantities to be used which best describe configurations, motions or constraints, and it yields equations of motion in concise forms. Examples are presented to illustrate the use and effectiveness of the approach. The objective of this paper is to provide a general geometric perspective of the governing equations of motion, and explain its suitability for studying complex dynamic systems subject to non-holonomic constraints.


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