no. 1
Jet bundle geometry, dynamical connections, and the inverse problem of lagrangian mechanics
Annales de l'I.H.P. Physique théorique, Tome 61 (1994) no. 1, pp. 17-62 
@article{AIHPA_1994__61_1_17_0,
     author = {Massa, Enrico and Pagani, Enrico},
     title = {Jet bundle geometry, dynamical connections, and the inverse problem of lagrangian mechanics},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {17--62},
     year = {1994},
     publisher = {Gauthier-Villars},
     volume = {61},
     number = {1},
     mrnumber = {1303184},
     zbl = {0813.70004},
     language = {en},
     url = {https://www.numdam.org/item/AIHPA_1994__61_1_17_0/}
}
TY  - JOUR
AU  - Massa, Enrico
AU  - Pagani, Enrico
TI  - Jet bundle geometry, dynamical connections, and the inverse problem of lagrangian mechanics
JO  - Annales de l'I.H.P. Physique théorique
PY  - 1994
SP  - 17
EP  - 62
VL  - 61
IS  - 1
PB  - Gauthier-Villars
UR  - https://www.numdam.org/item/AIHPA_1994__61_1_17_0/
LA  - en
ID  - AIHPA_1994__61_1_17_0
ER  - 
%0 Journal Article
%A Massa, Enrico
%A Pagani, Enrico
%T Jet bundle geometry, dynamical connections, and the inverse problem of lagrangian mechanics
%J Annales de l'I.H.P. Physique théorique
%D 1994
%P 17-62
%V 61
%N 1
%I Gauthier-Villars
%U https://www.numdam.org/item/AIHPA_1994__61_1_17_0/
%G en
%F AIHPA_1994__61_1_17_0
Massa, Enrico; Pagani, Enrico. Jet bundle geometry, dynamical connections, and the inverse problem of lagrangian mechanics. Annales de l'I.H.P. Physique théorique, Tome 61 (1994) no. 1, pp. 17-62. https://www.numdam.org/item/AIHPA_1994__61_1_17_0/

[1] M. Crampin, G.E. Prince and G. Thompson, A Geometrical Version of the Helmholtz Conditions in Time-Dependent Lagrangian Dynamics, J. Phys. A: Math. Gen., Vol. 17, 1984, pp. 1437-1447. | Zbl | MR

[2] E. Masssa and E. Pagani, Classical Dynamics of Non-holonomic Systems: a Geometric Approach, Ann. Inst. H. Poincaré, Vol. 55, 1991, pp. 511-544. | Numdam | Zbl | MR | EuDML

[3] M. De León and P.R. Rodrigues, Methods of Differential Geometry in Analytical Mechanics, North Holland, Amsterdam, 1989. | Zbl | MR

[4] D.J. Saunders, The Geometry of Jet Bundles, London Mathematical Society, Lecture Note Series 142, Cambridge University Press, 1989. | Zbl | MR

[5] W. Sarlet, Symmetries, First Integrals and the Inverse Problem of Lagrangian Mechanics, J. Phys. A: Math. Gen., Vol. 14, 1981, pp. 2227-2238. | Zbl | MR

[6] W. Sarlet and F. Cantrijn, Symmetries, First Integrals and the Inverse Problem of Lagrangian Mechanics: II, J. Phys. A: Math. Gen., Vol. 16, 1983, pp. 1383-1396. | Zbl | MR

[7] M. Crampin, F. Cantrijn and W. Sarlet, Pseudo-Symmetries, Noether's Theorem and the Adjoint Equation, J. Phys. A: Math. Gen., Vol. 20, 1987, pp. 1365-1376. | Zbl | MR

[8] M. Crampin, G.E. Prince and W. Sarlet, Adjoint Symmetries for Time-Dependent Second Order Equations, J. Phys. A: Math. Gen., Vol. 23, 1990, pp. 1335-1347. | Zbl | MR

[9] G. Marmo, E.J. Saletan, A. Simoni and B. Vitale, Dynamical Systems, John Wiley & Sons, Chichester, 1985. | Zbl

[10] M. Crampin, On the Differential Geometry of the Euler-Lagrange Equations, and the Inverse Problem of Lagrangian Dynamics, J. Phys. A: Math. Gen., Vol. 14, 1981, pp. 2567-2575. | Zbl | MR

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

[12] W. Sarlet, The Helmholtz Condition Revisited. A New Approach to the Inverse Problem of Lagrangian Dynamics, J. Phys. A: Math. Gen., Vol. 15, 1982, pp. 1503-1517. | Zbl | MR

[13] 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. Reports, Vol. 188, 1990, pp. 147-284. | MR

[14] M. Henneaux and L.C. Shepley, Lagrangians for Spherically Symmetric Potentials, J. Math. Phys., Vol. 23, 1982, pp. 2101-2107. | Zbl | MR

[15] G. Caviglia, Dynamical Symmetries, First Integrals and the Inverse Problem of Lagrangian Dynamics, Inverse Problems, Vol. 1, 1985, pp. 13-17. | Zbl | MR

[16] G. Caviglia, Helmholtz Conditions, Covariance, and Invariance Identities, Int. J. Theor. Phys., Vol. 24, 1985, pp. 377-390. | Zbl | MR

[17] F. Cantrijn, M. Crampin and W. Sarlet, Evading the Inverse Problem for Second Order Ordinary Differential Equations by Using Additional Variables, Inverse Problems, Vol. 3, 1987, pp. 51-63. | Zbl | MR

[18] J.F. Cariñena and E. Martinez, Symmetry Theory and Lagrangian Inverse Problem for Time-Dependent Second Order Differential Equations, J. Phys. A: Math. Gen., Vol. 22, 1989, pp. 2659-2665. | Zbl | MR

[19] W. Sarlet, Note on Equivalent Lagrangians and Symmetries, J. Phys. A: Math. Gen., Vol. 16, 1983, pp. 229-233. | Zbl | MR

[20] G. Marmo, N. Mukunda and J. Samuel, Dynamics and Symmetries for Constrained Systems: A Geometric Analysis, La Rivista del Nuovo Cimento, Vol. 6, 1983, 2, pp. 1-62. | MR

[21] F. Cantrijn, J.F. Cariñena, M. Crampin and L.A. Ibort, Reduction of Degenerate Lagrangian Systems, J. G. P., Vol. 3, 1986, pp. 353-400. | Zbl | MR

[22] J.F. Cariñena and L.A. Ibort, Geometric Theory of the Equivalence of Lagrangians for Constrained Systems, J. Phys. A: Math. Gen., Vol. 18, 1985, pp. 3335-3341. | Zbl | MR

[23] G. Giachetta, Jet Methods in Non-holonomic Mechanics, J. Math. Phys., Vol. 33, 1992, pp. 1652-1665. | Zbl | MR

[24] H. Helmholtz, Über die Physikalische Bedeutung des Princips der Kleisten Wirkung, J. Reine Angew. Math., Vol. 100, 1887, p. 137. | JFM

[25] G. Darboux, Leçons sur la théorie générale des surfaces, Gauthier-Villars, Paris, 1894.

[26] J. Douglas, Solution of the Inverse Problem of the Calculus of Variations, Trans. Amer. Math. Soc., Vol. 30, 1941, pp. 71-128. | Zbl | MR | JFM

[27] M. Henneaux, Equations of Motion, Commutation Relations and Ambiguities in the Lagrangian Formalism, Ann. Phys., Vol. 140, 1982, pp. 45-64. | Zbl | MR

[28] J.F. Pommaret, Systems of Partial Differential Equations and Lie Pseudogroups, Gordon and Breach, New York, 1978. | Zbl | MR

[29] C. Godbillon, Géométrie différentielle et mécanique analytique, Hermann, Paris, 1969. | Zbl | MR

[30] S. Sternberg, Lectures on Differential Geometry, Prentice Hall, Englewood Cliffs, New Jersey, 1964. | Zbl | MR

[31] L. Mangiarotti and M. Modugno, Fibered Spaces, Jet Spaces and Connections for Field Theories, Proceedings of the International Meeting on Geometry and Physics, Florence, October 12-15, 1982, Pitagora, Bologna, 1983, pp. 135-165. | Zbl | MR

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

[33] P.L. Garciá, The Poincaré-Cartan Invariant in the Calculus of Variations, Symposia Mathematica, Vol. 14, 1974, pp. 219-246. | Zbl | MR

[34] S. Kobayashi and K. Nomizu, Foundations of Differentiel Geometry, J. Wiley & Sons, New York, 1963. | Zbl

[35] J. Grifone, Estructure presque tangente et connexions I, Ann. Inst. Fourier, Grenoble, Vol. 22, 3, 1972, pp. 287-334. | Zbl | MR | Numdam

[36] J. Grifone, Estructure presque tangente et connexions II, Ann. Inst. Fourier Grenoble, Vol. 22, 4, 1972, pp. 291-338. | Zbl | MR | Numdam

[37] W. Sarlet, F. Cantrijn and M. Crampin, A New Look at Second Order Equations and Lagrangian Mechanics, J. Phys. A: Math. Gen., Vol. 17, 1984, pp. 1999-2009. | Zbl | MR

[38] M. Crampin and G.E. Prince, Generalizing Gauge Variance for Spherically Symmetric Potentials, J. Phys. A: Math. Gen., Vol. 18, 1985, p. 2167-2175 | Zbl | MR