Journal of Applied Nonlinear Dynamics
Formulation of the Governing Equations of Motion of Dynamic Systems on a Principal Bundle
Journal of Applied Nonlinear Dynamics 9(1) (2020) 129152  DOI:10.5890/JAND.2020.03.011
Xiaobo Liu
General Motors Company, 800 North Glenwood Ave., Pontiac, MI 48340, USA
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Abstract
In this paper, we present a geometric approach to form the governing equations of motion of dynamic systems. A geometric form of the d’AlembertLagrange 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 nonholonomic constraints.
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