The Hamilton-Cartan formalism in the calculus of variations
Hubert Goldschmidt; Shlomo Sternberg
Annales de l'institut Fourier (1973)
- Volume: 23, Issue: 1, page 203-267
- ISSN: 0373-0956
Access Full Article
topAbstract
topHow to cite
topReferences
top- [1] C. CARATHEODORY, Variationsrechnung und partielle Differential-gleichungen erster Ordnung, Teubner, Leipzig, 1935. Zbl0011.35603JFM61.0547.01
- [2] E. CARTAN, Leçons sur les invariants intégraux, Hermann, Paris, 1922. JFM48.0538.02
- [3] Th. De DONDER, Théorie invariantive du calcul des variations, Hayez, Brussels, 1935. Zbl0013.16901
- [4] H. GOLDSCHMIDT, Integrability criteria for systems of non-linear partial differential equations, J. Differential Geometry, 1 (1967), 269-307. Zbl0159.14101MR37 #1746
- [5] R. HERMANN, Differential geometry and the calculus of variations, Academic Press, New York, London, 1968. Zbl0219.49023MR38 #1635
- [6] E.L. HILL, Hamilton's principle and the conservation theorems of mathematical physics, Rev. Modern Phys., 23 (1951), 253-260. Zbl0044.38509MR13,503g
- [7] Th. LEPAGE, Sur les champs géodésiques du calcul des variations, Acad. Roy. Belg. Bull. Cl. Sci., (5) 22 (1936), 716-729, 1036-1046 ; Sur le champ géodésique des intégrales multiples, Acad. Roy. Belg. Bull. Cl. Sci., (5) 27 (1941), 27-46 ; Champs stationnaires, champs géodésiques et formes intégrables, Acad. Roy. Belg. Bull. Cl. Sci., (5) 28 (1942), 73-92, 247-265. Zbl0016.26201JFM62.1329.01
- [8] J. MILNOR, Morse Theory, Annals of Mathematics Studies, n° 51, Princeton University Press. Princeton, N. J., 1963. Zbl0108.10401
- [9] C.B. MORREY, Jr., Multiple integrals in the calculus of variations, Springer-Verlag, Berlin, Heidelberg, New York, 1966. Zbl0142.38701MR34 #2380
- [10] S. SMALE, On the Morse index theorem, J. Math. Mech., 14 (1965), 1049-1055. Zbl0166.36102MR31 #6251
- [11] S. STERNBERG, Lectures on differential geometry, Prentice Hall, Englewood Cliffs, N. J., 1964. Zbl0129.13102MR33 #1797
- [12] L. VAN HOVE, Sur la construction des champs de De Donder-Weyl par la méthode des caractéristiques, Acad. Roy. Belg. Bull. Cl. Sci., (5) 31 (1945), 278-285. Zbl0033.12202
- [13] H. WEYL, Geodesic fields in the calculus of variations for multiple integrals, Ann. of Math., 36 (1935), 607-629. Zbl0013.12002JFM61.0554.04
Citations in EuDML Documents
top- Hubert Goldschmidt, Le formalisme de Hamilton-Cartan en calcul des variations
- A. Echeverría Enríquez, M. C. Muñoz Lecanda, Variational calculus in several variables : a hamiltonian approach
- L. Mangiarotti, M. Modugno, Some results on the calculus of variations on jet spaces
- Mauro Francaviglia, Demeter Krupka, The hamiltonian formalism in higher order variational problems
- Ivan Kolář, Fundamental vector fields on associated fiber bundles
- Demeter Krupka, A map associated to the Lepagian forms on the calculus of variations in fibred manifolds
- Emanuel López, Alberto Molgado, José A. Vallejo, The principle of stationary action in the calculus of variations
- Jordi Gaset, Pedro D. Prieto-Martínez, Narciso Román-Roy, Variational principles and symmetries on fibered multisymplectic manifolds
- Michel Bauderon, Le problème inverse du calcul des variations
- Josef Janyška, On the Lie algebra of vertical prolongation operators