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TECHNICAL PAPERS

On the Transformation Properties of the Nonlinear Hamel Equations

[+] Author and Article Information
J. G. Papastavridis

School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0405

J. Appl. Mech 62(4), 924-929 (Dec 01, 1995) (6 pages) doi:10.1115/1.2896023 History: Received February 01, 1994; Revised September 27, 1994; Online October 30, 2007

Abstract

This paper discusses the transformation properties of the famous Johnsen-Hamel equations of motion of discrete mechanical systems in general nonlinear nonholonomic coordinates and constraints (i.e., the nonlinear extension of the well-known Boltzmann-Hamel equations), under general nonlinear (local) quasi-velocity transformations. It is shown that the individual kinematico-inertial terms making up the system inertia force, or system acceleration, such as the nonlinear nonholonomic Euler-Lagrange operator and nonholonomic correction (or deviation) terms, in general, do not transform as nonholonomic covariant vectors; although taken as a whole they do, as expected. This work extends and completes the work of Papastavridis (1994), and it is strongly recommended that it be read after that paper.

Copyright © 1995 by The American Society of Mechanical Engineers
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