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RESEARCH PAPERS

On Energy Rate Theorems for Linear First-Order Nonholonomic Systems

[+] Author and Article Information
John G. Papastavridis

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

J. Appl. Mech 58(2), 536-544 (Jun 01, 1991) (9 pages) doi:10.1115/1.2897217 History: Received February 20, 1989; Revised December 13, 1989; Online March 31, 2008

Abstract

Starting with the Boltzmann/Hamel equations of motion of mechanical systems subject to general linear and first-order nonholonomic and rheonomic constraints, and in nonholonomic coordinates, this paper derives the general (reactionless) energy rate, or power, equation for such systems, in a straightforward and physically clear fashion. A power (reaction-containing) equation for these systems, but in holonomic coordinates, is also derived for completeness. An example of a sphere rolling on a uniformly spinning plane serves to illustrate these power theorems. The paper extends and corrects the recent work by Kane and Levinson (1988) on the same topic.

Copyright © 1991 by The American Society of Mechanical Engineers
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