A constant of motion in 3D implies a local generalized Hamiltonian structure

Physics Letters, Section A: General, Atomic and Solid State Physics

Volumn 234, Issue 1, 1997, Pages 35-40

  Hernández Bermejo, Benito ^a   Fairén, Víctor ^a  

^a UNIVERSIDAD NACIONAL DE EDUCACIÓN A DISTANCIA   (Spain)

Author keywords

Generalized Hamiltonian structures; Ordinary differential equations; Poisson systems

Indexed keywords

ORDINARY DIFFERENTIAL EQUATIONS; PHASE SPACE METHODS; VECTOR SPACES;

3D VECTORS; CONSTANT OF MOTION; DIFFEOMORPHISMS; GENERALIZED HAMILTONIANS; NONAUTONOMOUS; POISSON STRUCTURE; POISSON SYSTEM;

HAMILTONIANS;

EID: 0001902093     PISSN: 03759601     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0375-9601(97)00558-6     Document Type: Article

References (33)

1. P.J. Olver, Applications of Lie Groups to Differential Equations, 2nd Ed. (Springer, New York, 1993).
2. A. Weinstein, J. Diff. Geom. 18 (1983) 523.
3. V. Perlick, J. Math. Phys. 33 (1992) 599.
4. L. Cairó and M.R. Feix, J. Phys. A 25 (1992) L1287.
5. H. Gümral and Y. Nutku, J. Math. Phys. 34 (1993) 5691.
6. F. Haas and J. Goedert, Phys. Lett. A 199 (1995) 173.
7. J. Goedert, F. Haas, D. Hua, M.R. Feix and L. Cairó, J. Phys. A 27 (1994) 6495.
8. C.A. Lucey and E.T. Newman, J. Math. Phys. 29 (1988) 2430.
9. S.A. Hojman, J. Phys. A 24 (1991) L249.
10. S.A. Hojman, J. Phys. A 29 (1996) 667.
11. Y. Nambu, Phys. Rev. D 7 (1973) 2405.
12. M. Razavy and F.J. Kennedy, Can. J. Phys. 52 (1974) 1532.
13. G.J. Ruggeri, Int. J. Theor. Phys. 12 (1975) 287.
14. J.A. Kobussen, Hadronic J. 1 (1978) 966.
15. E.T. Whittaker, A Treatrise on the Analytical Dynamics of Particles and Rigid Bodies, 4th Ed. (Cambridge Univ. Press, Cambridge, 1937).
16. R.M. Santilli, Foundations of Theoretical Mechanics, Vol. II (Springer, New York, 1983).
17. D.D. Holm and K.B. Wolf, Physica D 51 (1991) 189.
18. V.I. Arnold, Ann. Inst. Fourier Grenoble 16 (1966) 319.
19. D.D. Holm, J.E. Marsden, T. Ratiu and A. Weinstein, Phys. Rep. 123 (1985) 1.
20. J. Hofbauer, J. Math. Biol. 34 (1996) 675.
21. D. Chinea, J.C. Marrero and M. de León, J. Phys. A 29 (1996) 6313.
22. H. Yoshida, Phys. Lett. A 150 (1990) 262.
23. M. Sanz-Serna and M.P. Calvo, Numerical Hamiltonian Problems (Chapman & Hall, London, 1994).
24. G.R.W. Quispel and H.W. Capel, Phys. Lett. A 218 (1996) 223.
25. G.R.W. Quispel and G.S. Turner, J. Phys. A 29 (1996) L341.
26. E.A. Jackson, Perspectives of Nonlinear Dynamics, Vol. 1, 1st Ed. (Cambridge University Press, Cambridge, 1994).
27. M. Plank, J. Math. Phys. 36 (1995) 3520.
28. E.C.G. Sudarshan and N. Mukunda, Classical Mechanics - A Modern Perspective, 2nd Ed. (Krieger, New York, 1983).
29. M. Plank, Nonlinearity 9 (1996) 887.
30. Y. Nutku, Phys. Lett. A 145 (1990) 27.
31. Y. Nutku, J. Phys. A 23 (1990) L1145.
32. E.H. Kerner, J. Math. Phys. 22 (1981) 1366.
33. B. Hernández-Bermejo and V. Fairén, Phys. Lett. A 206 (1995) 31.