Technical Briefs

An Argument Against Augmenting the Lagrangean for Nonholonomic Systems

[+] Author and Article Information
Carlos M. Roithmayr2

 NASA Langley Research Center, Hampton, VA 23681c.m.roithmayr@larc.nasa.gov

Dewey H. Hodges

School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30332dhodges@gatech.edu


Corresponding author.

J. Appl. Mech 76(3), 034501 (Mar 09, 2009) (3 pages) doi:10.1115/1.3086435 History: Received June 28, 2007; Revised December 29, 2008; Published March 09, 2009

Although it is known that correct dynamical equations of motion for a nonholonomic system cannot be obtained from a Lagrangean that has been augmented with a sum of the nonholonomic constraint equations weighted with multipliers, previous publications suggest otherwise. One published example that was proposed in support of augmentation purportedly demonstrates that an accepted method fails to produce correct equations of motion whereas augmentation leads to correct equations. This present paper shows that, in fact, the opposite is true. The correct equations, previously discounted on the basis of a flawed application of the Newton–Euler method, are verified by using Kane’s method together with a new approach for determining the directions of constraint forces.

Copyright © 2009 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

A particle moving on a sliding inclined rod



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