The d’Alembert–Lagrange equation exploited on a Riemannian manifold

In this paper, we present a geometric exploitation of the d’Alembert–Lagrange equation (or alternatively, Lagrange form of the d’Alembert’s principle) on a Riemannian manifold. We develop the d’Alembert–Lagrange equation in a geometric form, as well as an explicit analytic form with respect to an ar...

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Bibliographic Details
Published inMultibody system dynamics Vol. 25; no. 4; pp. 411 - 427
Main Authors Liu, Xiaobo, Huston, R. L., Liu, C. Q.
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.04.2011
Subjects
Automotive Engineering
Control
Dynamical Systems
Electrical Engineering
Engineering
Mechanical Engineering
Optimization
Vibration
d’Alembert–Lagrange equation
Riemannian manifold
Nonholonomic systems
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Summary:In this paper, we present a geometric exploitation of the d’Alembert–Lagrange equation (or alternatively, Lagrange form of the d’Alembert’s principle) on a Riemannian manifold. We develop the d’Alembert–Lagrange equation in a geometric form, as well as an explicit analytic form with respect to an arbitrary frame in a coordinate neighborhood on the configuration manifold. We provide a procedure to determine the governing dynamic equations of motion. Examples are given to illustrate the new formulation of dynamic equations and their relations to alternative ones. The objective is to provide a generalized perspective of governing equations of motion and its suitability for studying complex dynamic systems subject to nonholonomic constraints.
ISSN:1384-5640
1573-272X
DOI:10.1007/s11044-010-9231-x