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Orthogonal projections and the dynamics of constrained mechanical systems
Author(s):
Paula
Balseiro;
Jorge
E.
Solomin
Journal:
Quart. Appl. Math.
66
(2008),
437-446.
MSC (2000):
Primary 70F25, 70H45, 70G45
Posted:
June 4, 2008
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Abstract:
A coordinate-free version of the approach to mechanical systems with non-ideal restrictions developed by Udwadia (2002) and Udwadia and Kalaba (2002) in a series of articles is introduced. Some of its properties are then reinterpreted in a general geometric setting in terms of orthogonal projections. A geometric view of other aspects of constrained systems, inspired by their insight, is also presented.
References:
-
- 1.
- J.E. Solomin and M. Zuccalli, A geometric approach to the extended D'Alembert principle of Udwadia-Kalaba-Hee-Chang. Quart. Appl. Math. 63, 269-275 (2005). MR 2150773 (2006a:70043)
- 2.
- F.E. Udwadia, Fundamental principles and Lagrangian dynamics: Mechanical systems with non-ideal, holonomic, and nonholonomic constraints. J. Math. Anal. Appl. 251, 341 (2002). MR 1790412 (2001j:70014)
- 3.
- F.E. Udwadia, On Constrained Motion. Applied Mathematics and Computation. 164, 313-320 (2005). MR 2131158 (2005m:70071)
- 4.
- F.E. Udwadia and R.E. Kalaba, On the foundations of analytical dynamics. Internat. J. Non-linear Mech. 37, 1079-1090 (2002), and references therein. MR 1897289 (2003f:70023)
- 5.
- F.E. Udwadia and R.E. Kalaba, What is the General Form of the Explicit Equations of Motion for Constrained Mechanical Systems? Journ. Applied Mechanics, 69, 335-339 (2002). MR 2000941 (2004g:70038)
- 6.
- 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). MR 1447580 (98f:70016)
- 7.
- A.M. Vershik, Classical and non-classical dynamics with constraints. Lecture Notes in Mathematics 1108, 278-301, Springer-Verlag 1984.
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Additional Information:
Paula
Balseiro
Affiliation:
Departmento de Matemática, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, Argentina
Email:
poi@mate.unlp.edu.ar
Jorge
E.
Solomin
Affiliation:
Departmento de Matemática, Facultad de Ciencias Exactas, Universidad Nacional de La Plata and Conicet, Argentina
Email:
solo@mate.unlp.edu.ar
PII:
S0033-569X-08-01104-1
Keywords:
Constrained mechanical systems,
geometric approach
Received by editor(s):
December 29, 2006
Posted:
June 4, 2008
Additional Notes:
The first author was supported in part by a fellowship of CONICET
Copyright of article:
Copyright
2008,
Brown University
The copyright for this article reverts to public domain after 28 years from publication.
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