On First-Order Decoupling of Equations of Motion for Constrained Dynamical Systems

[+] Author and Article Information
T. A. Loduha, B. Ravani

Department of Mechanical and Aeronautical Engineering, University of California, Davis, CA 95616-5294

J. Appl. Mech 62(1), 216-222 (Mar 01, 1995) (7 pages) doi:10.1115/1.2895905 History: Received February 22, 1993; Revised May 27, 1993; Online October 30, 2007


In this paper we present a method for obtaining first-order decoupled equations of motion for multirigid body systems. The inherent flexibility in choosing generalized velocity components as a function of generalized coordinates is used to influence the structure of the resulting dynamical equations. Initially, we describe how a congruency transformation can be formed that represents the transformation between generalized velocity components and generalized coordinate derivatives. It is shown that the proper choice for the congruency transformation will insure generation of first-order decoupled equations of motion for holonomic systems. In the case of nonholonomic systems, or holonomic systems with unreduced configuration coordinates, we incorporate an orthogonal complement in conjunction with the congruency transformation. A pair of examples illustrate the results. Finally, we discuss numerical implementation of congruency transformations to achieve first-order decoupled equations for simulation purposes.

Copyright © 1995 by The American Society of Mechanical Engineers
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