Symmetries and constants of the motion for dynamics in implicit form
G. Marmo; G. Mendella; W. M. Tulczyjew
Annales de l'I.H.P. Physique théorique (1992)
- Volume: 57, Issue: 2, page 147-166
- ISSN: 0246-0211
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topMarmo, G., Mendella, G., and Tulczyjew, W. M.. "Symmetries and constants of the motion for dynamics in implicit form." Annales de l'I.H.P. Physique théorique 57.2 (1992): 147-166. <http://eudml.org/doc/76582>.
@article{Marmo1992,
author = {Marmo, G., Mendella, G., Tulczyjew, W. M.},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {symmetries; singular Lagrangian; implicit differential equations; conservation laws; generalized Hamilton systems},
language = {eng},
number = {2},
pages = {147-166},
publisher = {Gauthier-Villars},
title = {Symmetries and constants of the motion for dynamics in implicit form},
url = {http://eudml.org/doc/76582},
volume = {57},
year = {1992},
}
TY - JOUR
AU - Marmo, G.
AU - Mendella, G.
AU - Tulczyjew, W. M.
TI - Symmetries and constants of the motion for dynamics in implicit form
JO - Annales de l'I.H.P. Physique théorique
PY - 1992
PB - Gauthier-Villars
VL - 57
IS - 2
SP - 147
EP - 166
LA - eng
KW - symmetries; singular Lagrangian; implicit differential equations; conservation laws; generalized Hamilton systems
UR - http://eudml.org/doc/76582
ER -
References
top- [1] R. Abraham and J.E. Marsden, Foundations of Mechanics, Benjamin, Mass. 1978. Zbl0393.70001MR515141
- [2] J.L. Anderson and P.G. Bergmann, Constraints in Covariant Field Theories, Phys. Rev., Vol. 83, 1951, pp.1018-1026. Zbl0045.45505MR44382
- [3] V.I. Arnold, Geometrical Methods in the Theory of Ordinary Differential Equations, Springer-Verlag, XI, New York, Heidelberg, Berlin, 1983. Zbl0507.34003MR695786
- [4] V.I. Arnold, A. Varchenko and S. Goussein-Zadé Eds., Singularités des applications differentiables, I, Editions Mir, Moscou, 1986.
- [5] V.I. Arnold Ed., Dynamical Systems, III, Springer-Verlag, New York, Heidelberg, Berlin, 1988. MR1292465
- [6] D.V. Asonov and V.I. Arnold Eds., Dynamical Systems, I, Springer-Verlag, New York, Heidelberg, Berlin, 1987. Zbl0658.00008MR970793
- [7] P.G. Bergmann and J. Goldberg, Dirac Bracket Transformations in Phase Space, Phys. Rev., Vol. 98, 1955, pp.531-538. Zbl0065.22803MR74314
- [8] F. Cantrijn, M. Crampin, W. Sarlet and D. Saunders, The Canonical Isomorphism Between TkT*M and T*TkM, C. R. Acad. Sci. Paris, T. 309, Serie II, 1989, pp.1509- 1514. Zbl0702.58006MR1033091
- [9] Y. Choquet-Bruhat, C. de Witt-Morette and M. Dillard-Bleick, Analysis, Manifolds and Physics, North-Holland, Amsterdam, Oxford, New York, Tokio, 1982. Zbl0492.58001MR678940
- [10] M. Crampin, Tangent Bundle Geometry for Lagrangian Dynamics, J. Phys. A: Math. Gen., Vol. 16, 1983, pp. 3755-3772. Zbl0536.58004MR727054
- [11] M. Crampin, F. Cantrijn and W. Sarlet, Lifting Geometric Objects to a Cotangent Bundle, and the Geometry of the Cotangent Bundle of a Tangent Bundle, J. Geom. Phys., Vol. 4, 1987, pp.469-492. Zbl0699.53042MR986419
- [12] P.A.M. Dirac, Generalized Hamiltonian Dynamics, Can. J. Math., Vol. 2, 1950, pp.129-148. Zbl0036.14104MR43724
- [13] P.A.M. Dirac, Lectures in Quantum Mechanics, Belfer Graduate School of Science, Yeshiva University, New York, 1967.
- [14] A. Frölicher and A. Nijenhuis, Theory of vector valued differential forms, Nederl. Akad. Wetensch. Proc., Vol. A 59, 1956, pp.338-359. Zbl0079.37502MR82554
- [15] J. Klein, On Lie Algebras of Vector Fields defined by Vector Forms, Colloquia Mathematica Societatis Janos Bolyai, 46, Topics in Differential Geometry, Debrecen, Hungary, 1984. Zbl0646.58002
- [16] P. Libermann and C.M. Marle, Symplectic Geometry and Analytical Mechanics, Reidel D, Dordrecht, 1987. Zbl0643.53002MR882548
- [17] L. Lusanna, An Enlarged Phase Space for Finite-dimensional Constrained Systems, Unifying Their Lagrangian, Phase- and Velocity-space Descriptions, Physics Reports, Vol. 185, 1990, pp.1-54. MR1034469
- [18] G. Marmo, E.J. Saletan, A. Simoni and B. Vitale, Dynamical Systems. A Differential Geometric Approach to Symmetry and Reduction, Wiley, New York, 1985. Zbl0592.58031MR818988
- [19] M.R. Menzio and W.M. Tulczyjew, Infinitesimal Symplectic Relations and Generalized Hamiltonian Dynamics, Ann. Inst. H. Poincaré, Vol. A28, 1978, pp.349-367. Zbl0405.58029MR511066
- [20] G. Morandi, C. Ferrario, G. Lo Vecchio, G. Marmo and C. Rubano, The Inverse Problem in the Calculus of Variations and the Geometry of the Tangent Bundle, Phys. Rep., Vol. 188, 1990, pp.147-284. Zbl1211.58008MR1050526
- [21] G. Pidello and W.M. Tulczyjew, Derivations of differential forms on Jet Bundles, Ann. Matem. Pura e Applic., Vol. 147, 1987, pp.249-265. Zbl0642.58004MR916711
- [22] E.C.G. Sudarshan and N. Mukunda, Classical Dynamics: A Modern Perspective, Wiley, New York, 1974. Zbl0329.70001MR434047
- [23] W.M. Tulczyjew, Hamiltonian Systems, Lagrangian Systems and the Legendre Transformation, Symp. Math., Vol. 16, 1974, pp.247-258. Zbl0304.58015MR388451
- [24] W.M. Tulczyjew, Sur la différentielle de Lagrange, C. R. Acad. Sci. Paris, T. 280, 1975, pp.1295-1298. Zbl0314.58018MR377987
- [25] W.M. Tulczyjew, The Lagrange Differential, Bull. Acad. Pol. des Sciences, Vol. 24, 1976, pp.1089-1096. Zbl0352.58002MR650306
- [26] W.M. Tulczyjew, Le sous-varietes Lagrangiennes et la dynamique Hamiltonienne, C. R. Acad. Sci. Paris, T. 283, 1976, p. 15. Zbl0327.58007MR420714
- [27] W.M. Tulczyjew, Le sous-varietes Lagrangiennes et la dynamique Lagrangienne, C. R. Acad. Sci. Paris, T. 283, 1976, pp. 675-678. Zbl0334.58008MR420715
- [28] W.M. Tulczyjew, The Legendre Transformation, Ann. Int. H. Poincaré, Vol. 27, 1977, pp. 101-114. Zbl0365.58011MR494271
- [29] W.M. Tulczyjew, A Symplectic Formulation of Relativistic Particle Dynamics, Acta Phys. Pol., Vol. B8, 1977, pp.431-447. MR445547
- [30] W.M. Tulczyjew, Geometrical Formulations of Physical Theories, Bibliopolis, Napoli, 1989. Zbl0707.58001MR1026453
- [31] A. Weinstein, Lectures on Symplectic Manifolds, American Math. Soc., Providence, R.I., 1977. Zbl0406.53031MR464312
- [32] K. Yano and S. Ishihara, Tangent and Cotangent Bundles, Dekker, New York, 1973. Zbl0262.53024MR350650
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