0
Research Papers

Hamel Paradox and Rosenberg Conjecture in Analytical Dynamics

[+] Author and Article Information
Y. H. Chen

Professor
The George W. Woodruff School of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
e-mail: yehwa.chen@me.gatech.edu

Manuscript received March 9, 2011; final manuscript received October 5, 2012; accepted manuscript posted October 22, 2012; published online May 16, 2013. Assoc. Editor: Alexander F. Vakakis.

J. Appl. Mech 80(4), 041001 (May 16, 2013) (8 pages) Paper No: JAM-11-1076; doi: 10.1115/1.4007861 History: Received March 09, 2011; Revised October 05, 2012; Accepted October 22, 2012

Hamel proposed a seemingly intuitive, simple, straightforward, but incorrect, method of formulating the constrained equation of motion. The method has to do with the direct embedding of the constraint into the kinetic energy of the unconstrained motion. His intention was to caution against its possible adoption. Rosenberg echoed Hamel's warning and followed up to explore more insight of this method. He proposed a conjecture that the Hamel's embedding method would work if the constraint was holonomic. It would not work if the constraint was nonholonomic. We investigate the Hamel paradox and Rosenberg conjecture via the use of the Fundamental Equation of Constrained Motion.

Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.

References

Hamel, G., 1949, Theoretische Mechanik, Springer, Berlin.
Papastavridis, J. G., 2002, Analytical Mechanics: A Comprehensive Treatise on the Dynamics of Constrained Systems; For Engineers, Physicists, and Mathematicians, Oxford University Press, New York.
Udwadia, F. E., and Wanichanon, T., 2010, “Hamel's Paradox and the Foundations of Analytical Dynamics,” Appl. Math. Comput., 217, pp. 1253–1265. [CrossRef]
Rosenberg, R. M., 1977, Analytical Dynamics of Discrete Systems, Plenum Press, New York.
Kalaba, R. E., and Udwadia, F. E., 1994, “Lagrangian Mechanics, Gauss's Principle, Quadratic Programming, and Generalized Inverses: New Equations of Motion for Nonholonomically Constrained Discrete Mechanical Systems,” Q. Appl. Math., 52(2), pp. 229–241.
Udwadia, F. E., and Kalaba, R. E., 1995, “An Alternate Proof for the New Equations of Motion for Constrained Mechanical Systems,” Appl. Math. Comput., 70, pp. 339–342. [CrossRef]
Udwadia, F. E., Kalaba, R. E., and Eun, H. C., 1997, “Equations of Motion for Constrained Mechanical Systems and the Extended D'Alembert Principle,” Q. Appl. Math., 56 (2), pp. 321–331.

Figures

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In