Research Papers

Hamel Paradox and Rosenberg Conjecture in Analytical Dynamics

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

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.

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