A geometric approach to the extended D’Alembert principle of Udwadia-Kalaba-Hee-Chang
Authors:
Jorge E. Solomin and Marcela Zuccalli
Journal:
Quart. Appl. Math. 63 (2005), 269-275
MSC (2000):
Primary 70F25; Secondary 70H45, 70G45
DOI:
https://doi.org/10.1090/S0033-569X-05-00944-7
Published electronically:
April 7, 2005
MathSciNet review:
2150773
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Abstract: The extended D’Alembert Principle introduced by Udwadia, Kalaba, and Hee-Chang (1997) is analyzed in the framework developed by Vershik and Fadeev (1981) and shown to be equivalent to the general version of the Principle of virtual work presented therein.
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- Firdaus E. Udwadia, Robert E. Kalaba, and Hee-Chang Eun, Equations of motion for constrained mechanical systems and the extended d’Alembert’s principle, Quart. Appl. Math. 55 (1997), no. 2, 321–331. MR 1447580, DOI https://doi.org/10.1090/qam/1447580
vf A.M. Vershik, Fadeev L., Lagrangian mechanics in invariant form, Selecta Math. Soviet. (1), 339-350 (1981).
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ap P. Appell, Traité de Méchanique Rationelle (troisième édition). Gauthier-Villars, 1911.
gps H. Goldstein, Ch. Poole, J. Safko, Classical Mechanics (third edition). Addison-Wesley, 2002.
n Ju.I Neimark, N.A. Fufaev, Dynamics of Nonholonomic Systems. AMS Translations of Mathematical Monographs, Vol. 33, 1972.
ukh F.E. Udwadia, R.E. Kalaba, E. Hee-Chang, Equations of motion for constrained mechanical systems and the extended D’Alembert principle, Quart. Appl. Math. (LV) 2, 321-331 (1997).
vf A.M. Vershik, Fadeev L., Lagrangian mechanics in invariant form, Selecta Math. Soviet. (1), 339-350 (1981).
wh E.T. Whittaker, A Treatise on the Analytical Dynamics of Particles and Rigid Bodies. Cambridge University Press, 1904.
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Additional Information
Jorge E. Solomin
Affiliation:
Universidad Nacional de La Plata, Departamento de Matemática, CC 172, 1900 La Plata, Argentina
Marcela Zuccalli
Affiliation:
Universidad Nacional de La Plata, Departamento de Matemática, Calle 50 esq 115, 1900 La Plata, Argentina
Received by editor(s):
April 8, 2003
Published electronically:
April 7, 2005
Article copyright:
© Copyright 2005
Brown University
