Lagrangian systems with higher order constraints

Journal of Mathematical Physics

Volumn 48, Issue 5, 2007, Pages

  Cendra, H ^a,b   Grillo, S D ^b,c  

^a UNIVERSIDAD NACIONAL DEL SUR   (Argentina)

^b Facultad de Ciencias Naturales e Instituto M Lillo   (Argentina)

^c INSTITUTO BALSEIRO   (Argentina)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34249896662     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2740470     Document Type: Article

References (32)

1. J. H. Greidanus, Report No. V 1038 (Nationaal Luchtvaartlaboratorium, Amsterdam, 1942).
2. Y. Rocard, Dynamique Ǵńrale des Vibrations (Masson et Cie Éditeurs, Paris, 1949), Chap., p. 246.
3. Y. Rocard, L'instabilit́ en Ḿcanique; Automobiles, Avions, Ponts Suspendus (Masson, Paris, 1954).
4. J. I. Neimark and N. A. Fufaev, Dynamics of Non-holonomic Systems, Translations of Mathematical Monographs Vol. 33 (AMS, Providence, 1972).
5. H. Cendra, A. Ibort, M. de León, and D. de Diego, J. Math. Phys. 45, 2785 (2004).
6. D. Shan, Prikl. Mat. Mekh. 37, 349 (1973).
7. O. Krupková, J. Math. Phys. 41, 5304 (2000).
8. H. Cendra and S. D. Grillo, J. Math. Phys. 47, 022902 (2006).
9. N. G. Chetaev, Izv. Fiz-Mat. Obsc. Kazan Univ. 7, 68 (1934).
10. V. Valcovici, Ber. Verh. Saechs. Akad. Wiss. Leipzig, Math.-Naturwiss. Kl. 102 (1958).
11. Y. Pironneau, in Proceedings of the IUTAM-ISIMMM Symposium on Modern Developments in Analytical Mechanics, Torino, 1982, edited by, S. Benenti, M. Francaviglia, and, A. Lichnerowicz, (Acta Academiae Scientiarum Taurinensis, Torino, 1983), pp. 671-686.
12. A. M. Vershik and L. D. Faddeev, Sov. Phys. Dokl. 0038-5689 17, 34 (1972); A. M. Vershik and L. D. Faddeev, Sel. Math. Sov. 1, 339 (1981).
13. A. M. Vershik and L. D. Faddeev, Sov. Phys. Dokl. 0038-5689 17, 34 (1972); A. M. Vershik and L. D. Faddeev, Sel. Math. Sov. 1, 339 (1981).
14. C.-M. Marle, Rend. Sem. Mat. Univ. Pol. Torino 54 (4), 353 (1996); C.-M. Marle, Rep. Math. Phys. 42, 211 (1998).
15. C.-M. Marle, Rend. Sem. Mat. Univ. Pol. Torino 54 (4), 353 (1996); C.-M. Marle, Rep. Math. Phys. 42, 211 (1998).
16. M. de León and P. R. Rodrigues, Generalized Classical Mechanics and Field Theory (North-Holland, Amsterdam, 1985).
17. M. Crampin, W. Sarlet, and F. Cantrijn, Math. Proc. Cambridge Philos. Soc. 99, 565 (1986).
18. L. Rayleigh, The Theory of Sound (Dover, New York, 1945).
19. E. T. Whittaker, A Treatise on the Analytical Dynamics of Particles and Rigid Bodies (Cambridge University Press, Cambridge, 1937).
20. H. Cendra, J. E. Marsden, and T. S. Ratiu, Lagrangian Reduction by Stages (American Mathematical Society, Providence, 2000).
21. H. Cendra, J. E. Marsden, and T. S. Ratiu, in Mathematics Unlimited-2001 and Beyond, edited by, B. Enguist, and, W. Schmid, (Springer-Verlag, New York, 2001), pp. 221-273.
22. J. Cort́s, Geometric Control and Numerical Aspects of Non-Holonomic Systems, Lecture Notes in Mathematics Vol. 1793 (Springer-Verlag, Berlin, 2003).
23. H. Cendra, S. Ferraro, and S. Grillo (unpublished).
24. F. Bullo and A. Lewis, Geometric Control of Mechanical Systems (Springer-Verlag, New York, 2005).
25. W. M. Tulczyjew and P. Urbanski, Acta Phys. Pol. B 30, 2909 (1999).
26. R. E. Gamboa Saraví and J. E. Solomin, J. Phys. A 36, 1 (2003).
27. H. Cendra, J. E. Marsden, S. Pekarsky, and T. S. Ratiu, Mosc. Math. J. 3, 833 (2003).
28. G. Marmo, W. M. Tulczyjew, and P. Urbanski, e-print arXiv:math-ph0104033.
29. F. Cantrijn, M. Crampin, W. Sarlet, and D. Saunders, C. R. Acad. Sci., Ser. II: Mec., Phys., Chim., Astron. 309, 1509 (1989).
30. M. de Ĺon and E. Vázquez-Abal, An. Univ. Bucuresti Mat. 34, 40 (1985); M. Djaa and J. Gancarzewicz, Cahiers Math 1, 3 (1986).
31. M. de Ĺon and E. Vázquez-Abal, An. Univ. Bucuresti Mat. 34, 40 (1985); M. Djaa and J. Gancarzewicz, Cahiers Math 1, 3 (1986).
32. A. Shiriaev, J. W. Perram, and C. Canudas-de-Wit, IEEE Trans. Autom. Control 50, 1164 (2005).