Orthogonal projections and the dynamics of constrained mechanical systems
Authors:
Paula Balseiro and Jorge E. Solomin
Journal:
Quart. Appl. Math. 66 (2008), 437-446
MSC (2000):
Primary 70F25, 70H45, 70G45
DOI:
https://doi.org/10.1090/S0033-569X-08-01104-1
Published electronically:
June 4, 2008
MathSciNet review:
2445522
Full-text PDF Free Access
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Additional Information
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
- Jorge E. Solomin and Marcela Zuccalli, A geometric approach to the extended D’Alembert principle of Udwadia-Kalaba-Hee-Chang, Quart. Appl. Math. 63 (2005), no. 2, 269–275. MR 2150773, DOI https://doi.org/10.1090/S0033-569X-05-00944-7
- Firdaus E. Udwadia, Fundamental principles of Lagrangian dynamics: mechanical systems with non-ideal, holonomic, and nonholonomic constraints, J. Math. Anal. Appl. 251 (2000), no. 1, 341–355. MR 1790412, DOI https://doi.org/10.1006/jmaa.2000.7050
- Firdaus E. Udwadia, On constrained motion, Appl. Math. Comput. 164 (2005), no. 2, 313–320. MR 2131158, DOI https://doi.org/10.1016/j.amc.2004.06.039
- F. E. Udwadia and R. E. Kalaba, On the foundations of analytical dynamics, Internat. J. Non-Linear Mech. 37 (2002), no. 6, 1079–1090. MR 1897289, DOI https://doi.org/10.1016/S0020-7462%2801%2900033-6
- F. E. Udwadia and R. E. Kalaba, What is the general form of the explicit equations of motion for constrained mechanical systems?, Trans. ASME J. Appl. Mech. 69 (2002), no. 3, 335–339. MR 2000941, DOI https://doi.org/10.1115/1.1459071
- 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
- A.M. Vershik, Classical and non-classical dynamics with constraints. Lecture Notes in Mathematics 1108, 278-301, Springer-Verlag 1984.
References
- 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)
- 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)
- F.E. Udwadia, On Constrained Motion. Applied Mathematics and Computation. 164, 313-320 (2005). MR 2131158 (2005m:70071)
- 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)
- 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)
- 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)
- 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
Keywords:
Constrained mechanical systems,
geometric approach
Received by editor(s):
December 29, 2006
Published electronically:
June 4, 2008
Additional Notes:
The first author was supported in part by a fellowship of CONICET
Article copyright:
© Copyright 2008
Brown University
The copyright for this article reverts to public domain 28 years after publication.
