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.

References

References
1.
Hamel
,
G.
,
1949
,
Theoretische Mechanik
,
Springer
,
Berlin
.
2.
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
.
3.
Udwadia
,
F. E.
, and
Wanichanon
,
T.
,
2010
, “
Hamel's Paradox and the Foundations of Analytical Dynamics
,”
Appl. Math. Comput.
,
217
, pp.
1253
1265
.10.1016/j.amc.2010.02.033
4.
Rosenberg
,
R. M.
,
1977
,
Analytical Dynamics of Discrete Systems
,
Plenum Press
,
New York
.
5.
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
.
6.
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
.10.1016/0096-3003(94)00113-I
7.
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
.
You do not currently have access to this content.