Le problème inverse du calcul des variations

Michel Bauderon

Annales de l'I.H.P. Physique théorique (1982)

  • Volume: 36, Issue: 2, page 159-179
  • ISSN: 0246-0211

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Bauderon, Michel. "Le problème inverse du calcul des variations." Annales de l'I.H.P. Physique théorique 36.2 (1982): 159-179. <http://eudml.org/doc/76151>.

@article{Bauderon1982,
author = {Bauderon, Michel},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {Euler-Lagrange system; infinite jet space; Helmholtz-Volterra conditions},
language = {fre},
number = {2},
pages = {159-179},
publisher = {Gauthier-Villars},
title = {Le problème inverse du calcul des variations},
url = {http://eudml.org/doc/76151},
volume = {36},
year = {1982},
}

TY - JOUR
AU - Bauderon, Michel
TI - Le problème inverse du calcul des variations
JO - Annales de l'I.H.P. Physique théorique
PY - 1982
PB - Gauthier-Villars
VL - 36
IS - 2
SP - 159
EP - 179
LA - fre
KW - Euler-Lagrange system; infinite jet space; Helmholtz-Volterra conditions
UR - http://eudml.org/doc/76151
ER -

References

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  1. [1] Abraham et Marsden, Foundations of Mechanics, 2nd edition (Benjamin). Zbl0393.70001
  2. [2] Bauderon, Thèse de troisième cycle, Université de Paris VI, 1980. 
  3. [3] Bourbaki, Variétés différentiables et analytiques. Fascicule de résultats, Hermann. Paris. Zbl0217.20401
  4. [4] Goldschmidt, Integrability criteria for partial differential equations, J. Diff. Geom., t. I, 1967, p. 269-307. Zbl0159.14101
  5. [5] Goldschmidt et Sternberg, Hamiltonian formalism in the calculus of variations. Ann. Ins. Fourier, t. 23, 1, 1973, p. 203-267. Zbl0243.49011MR341531
  6. [6] Horndecki, Differential operators associated with the Euler-Lagrange operator. Tensor N. S., t. 28, 1974. Zbl0289.49045MR356143
  7. [7] Kuperschmidt, Geometry of jet bundles and the structure of lagrangian and hamiltonian formalism, Geometrical methods in Mathematical physics, Lect. Notes n° 775, Springer-Verlag, 1980. Zbl0439.58016MR569303
  8. [8] Olver, On the hamiltonian structure of evolution equations, Math. Proc. Camb. Phil. Soc., t. 88, 1980, p. 71-88. Zbl0445.58012MR569634
  9. [9] Santilli, Foundations of theoretical mechanics I, Texts and monographs in physics, Springer-Verlag, 1978. Zbl0401.70015MR514210
  10. [10] Takens, Symmetries, conservations laws and variation al principle, Geometry and topology, Lect. Notes in Maths n° 597, Springer-Verlag. Zbl0368.49019
  11. [11] Takens, A global version of the inverse problem of the calculus of variations Preprint, Rijksuniversiteit Groningen, 1977. 
  12. [12] Tonti, Variational formulation of nonlinear differential equations (I), Bull. Sci. Acad. Roy. Belg., t. 55, 1969, p. 137-165. Zbl0182.11402MR256235
  13. [13] Tulczyjew, The Lagrange Complex. Bull. Soc. Math., France, t. 105, 1977, p. 419-431. Zbl0408.58020MR494272
  14. [14] Tulczyjew, The Euler-Lagrange resolution and TULCZYJEW et DEDECKER, Spectral sequences and the inverse problem of the calculus of variations, Differential Geometrical methods in Mathematical Physics, Lect. Notes in Maths n° 836, Springer-Verlag, 1980. p. 22-48 and p. 498-503. Zbl0456.58012MR607685
  15. [15] Vinogradov, On the algebro-geometric foundations of Lagrangian field Theory, Soviet. Math. Dokl., t. 18, 1977, p. 1200-1204. Zbl0403.58005
  16. [16] Vinogradov, A spectral sequence associated with a nonlinear differential equation, and algebro-geometric foundations of Lagrangian field theory with constraints, Soviet Math. Dokl., t. 19, 1977, p. 146-148. Zbl0406.58015

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