Symmetries and constants of the motion for dynamics in implicit form
Annales de l'I.H.P. Physique théorique, Tome 57 (1992) no. 2, pp. 147-166. 
@article{AIHPA_1992__57_2_147_0,
     author = {Marmo, G. and Mendella, G. and Tulczyjew, W. M.},
     title = {Symmetries and constants of the motion for dynamics in implicit form},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {147--166},
     publisher = {Gauthier-Villars},
     volume = {57},
     number = {2},
     year = {1992},
     mrnumber = {1184887},
     zbl = {0766.58020},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1992__57_2_147_0/}
}
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
SP  - 147
EP  - 166
VL  - 57
IS  - 2
PB  - Gauthier-Villars
UR  - http://www.numdam.org/item/AIHPA_1992__57_2_147_0/
LA  - en
ID  - AIHPA_1992__57_2_147_0
ER  - 
%0 Journal Article
%A Marmo, G.
%A Mendella, G.
%A Tulczyjew, W. M.
%T Symmetries and constants of the motion for dynamics in implicit form
%J Annales de l'I.H.P. Physique théorique
%D 1992
%P 147-166
%V 57
%N 2
%I Gauthier-Villars
%U http://www.numdam.org/item/AIHPA_1992__57_2_147_0/
%G en
%F AIHPA_1992__57_2_147_0
Marmo, G.; Mendella, G.; Tulczyjew, W. M. Symmetries and constants of the motion for dynamics in implicit form. Annales de l'I.H.P. Physique théorique, Tome 57 (1992) no. 2, pp. 147-166. http://www.numdam.org/item/AIHPA_1992__57_2_147_0/

[1] R. Abraham and J.E. Marsden, Foundations of Mechanics, Benjamin, Mass. 1978. | MR | Zbl

[2] J.L. Anderson and P.G. Bergmann, Constraints in Covariant Field Theories, Phys. Rev., Vol. 83, 1951, pp.1018-1026. | MR | Zbl

[3] V.I. Arnold, Geometrical Methods in the Theory of Ordinary Differential Equations, Springer-Verlag, XI, New York, Heidelberg, Berlin, 1983. | MR | Zbl

[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. | MR

[6] D.V. Asonov and V.I. Arnold Eds., Dynamical Systems, I, Springer-Verlag, New York, Heidelberg, Berlin, 1987. | MR | Zbl

[7] P.G. Bergmann and J. Goldberg, Dirac Bracket Transformations in Phase Space, Phys. Rev., Vol. 98, 1955, pp.531-538. | MR | Zbl

[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. | MR | Zbl

[9] Y. Choquet-Bruhat, C. De Witt-Morette and M. Dillard-Bleick, Analysis, Manifolds and Physics, North-Holland, Amsterdam, Oxford, New York, Tokio, 1982. | MR | Zbl

[10] M. Crampin, Tangent Bundle Geometry for Lagrangian Dynamics, J. Phys. A: Math. Gen., Vol. 16, 1983, pp. 3755-3772. | MR | Zbl

[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. | MR | Zbl

[12] P.A.M. Dirac, Generalized Hamiltonian Dynamics, Can. J. Math., Vol. 2, 1950, pp.129-148. | MR | Zbl

[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. | MR | Zbl

[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. | Zbl

[16] P. Libermann and C.M. Marle, Symplectic Geometry and Analytical Mechanics, Reidel D, Dordrecht, 1987. | MR | Zbl

[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. | MR

[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. | MR | Zbl

[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. | Numdam | MR | Zbl

[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. | MR

[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. | MR | Zbl

[22] E.C.G. Sudarshan and N. Mukunda, Classical Dynamics: A Modern Perspective, Wiley, New York, 1974. | MR | Zbl

[23] W.M. Tulczyjew, Hamiltonian Systems, Lagrangian Systems and the Legendre Transformation, Symp. Math., Vol. 16, 1974, pp.247-258. | MR | Zbl

[24] W.M. Tulczyjew, Sur la différentielle de Lagrange, C. R. Acad. Sci. Paris, T. 280, 1975, pp.1295-1298. | MR | Zbl

[25] W.M. Tulczyjew, The Lagrange Differential, Bull. Acad. Pol. des Sciences, Vol. 24, 1976, pp.1089-1096. | MR | Zbl

[26] W.M. Tulczyjew, Le sous-varietes Lagrangiennes et la dynamique Hamiltonienne, C. R. Acad. Sci. Paris, T. 283, 1976, p. 15. | MR | Zbl

[27] W.M. Tulczyjew, Le sous-varietes Lagrangiennes et la dynamique Lagrangienne, C. R. Acad. Sci. Paris, T. 283, 1976, pp. 675-678. | MR | Zbl

[28] W.M. Tulczyjew, The Legendre Transformation, Ann. Int. H. Poincaré, Vol. 27, 1977, pp. 101-114. | Numdam | MR | Zbl

[29] W.M. Tulczyjew, A Symplectic Formulation of Relativistic Particle Dynamics, Acta Phys. Pol., Vol. B8, 1977, pp.431-447. | MR

[30] W.M. Tulczyjew, Geometrical Formulations of Physical Theories, Bibliopolis, Napoli, 1989. | MR | Zbl

[31] A. Weinstein, Lectures on Symplectic Manifolds, American Math. Soc., Providence, R.I., 1977. | MR | Zbl

[32] K. Yano and S. Ishihara, Tangent and Cotangent Bundles, Dekker, New York, 1973. | MR | Zbl