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.
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An Argument Against Augmenting the Lagrangean for Nonholonomic Systems
Dewey H. Hodges
Dewey H. Hodges
Professor
School of Aerospace Engineering,
e-mail: dhodges@gatech.edu
Georgia Institute of Technology
, Atlanta, GA 30332
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Carlos M. Roithmayr
Dewey H. Hodges
Professor
School of Aerospace Engineering,
Georgia Institute of Technology
, Atlanta, GA 30332e-mail: dhodges@gatech.edu
J. Appl. Mech. May 2009, 76(3): 034501 (3 pages)
Published Online: March 9, 2009
Article history
Received:
June 28, 2007
Revised:
December 29, 2008
Published:
March 9, 2009
Citation
Roithmayr, C. M., and Hodges, D. H. (March 9, 2009). "An Argument Against Augmenting the Lagrangean for Nonholonomic Systems." ASME. J. Appl. Mech. May 2009; 76(3): 034501. https://doi.org/10.1115/1.3086435
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