Aspects of the inverse problem to the calculus of variations
Archivum Mathematicum (1988)
- Volume: 024, Issue: 4, page 181-202
- ISSN: 0044-8753
Access Full Article
topHow to cite
topAnderson, Ian M.. "Aspects of the inverse problem to the calculus of variations." Archivum Mathematicum 024.4 (1988): 181-202. <http://eudml.org/doc/18247>.
@article{Anderson1988,
author = {Anderson, Ian M.},
journal = {Archivum Mathematicum},
keywords = {Euler-Lagrange equations; Helmholtz equations; Cartan forms; Chern-Simons invariants; inverse problem; variational bicomplex; Noether's theorem},
language = {eng},
number = {4},
pages = {181-202},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Aspects of the inverse problem to the calculus of variations},
url = {http://eudml.org/doc/18247},
volume = {024},
year = {1988},
}
TY - JOUR
AU - Anderson, Ian M.
TI - Aspects of the inverse problem to the calculus of variations
JO - Archivum Mathematicum
PY - 1988
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 024
IS - 4
SP - 181
EP - 202
LA - eng
KW - Euler-Lagrange equations; Helmholtz equations; Cartan forms; Chern-Simons invariants; inverse problem; variational bicomplex; Noether's theorem
UR - http://eudml.org/doc/18247
ER -
References
top- S. J. Aldersley, G. W. Horndeski, Conformally invariant tensorial concomitants of a pseudo-Riemannian metric, Utilitas Math. 17 (1980), 197-223. (1980) Zbl0441.53011MR0583141
- I. M. Anderson, On the structure of divergence-free tensors, J. Math. Phys. 19 (1978), 2570-2575. (1978) Zbl0429.53048MR0512978
- I. M. Anderson, Tensorial Euler-Lagrange expressions and conservation laws, Aequationes Math. 17 (1978), 255-291. (1978) Zbl0418.49041MR0493675
- I. M. Anderson, Natural variational principles on Riemannian manifolds, Annals of Math. 120 (1984), 329-370. (1984) Zbl0565.58019MR0763910
- I. M. Anderson, The variational bicomplex, (to appear). Zbl0881.35069
- I. M. Anderson, The minimal order solution to the inverse problem, (to appear).
- I. M. Anderson, Natural differential operators on the variational bicomplex, (to appear).
- I. M. Anderson, T. Duchamp, On the existence of global variational principles, Amer. J. Math. 102 (1980), 781-868. (1980) Zbl0454.58021MR0590637
- I. M. Anderson, T. Duchamp, Variational principles for second order quasi-linear scalar equations, J. Diff. Eqs. 51 (1984), 1-47. (1984) Zbl0533.49010MR0727029
- D. E. Betounes, Extensions of the classical Cartan form, Phys. Rev. D 29 (1984), 599-606. (1984) MR0734285
- K. S. Cheng, W. T. Ni, Conditions for the local existence of metric in a generic affine manifold, Math. Proc. Camb. Phil. Soc. 87 (1980), 527-534. (1980) Zbl0442.53020MR0556932
- S. S. Chern, J. Simons, Characteristic forms and geometric invariants, Annals of Math. 99 (1974), 48-69. (1974) Zbl0283.53036MR0353327
- M. Crampin, Alternative Lagrangians in particle dynamics, (to appear). Zbl0666.58022MR0923340
- V. V. Dodonov V. I. Man'ko, V. D. Skarzhinsky, The inverse problem of the variational calculus and the nonuniqueness of the quantization of classical systems, Hadronic J. 4 (1981), 1734-1803. (1981) MR0632443
- V. V. Dodonov V. I. Man'ko, V. D. Skarzhinsky, Classically equivalent Hamiltonians and ambiguities of quantization: a particle in a magnetic field, Il Nuovo Cimento 69B (1982), 185-205. (1982) MR0669159
- J. Douglas, Solution to the inverse problem of the calculus of variations, Trans. Amer. Math. Soc. 50 (1941), 71-128. (1941) MR0004740
- M. Ferraris, Fibered connections and Global Poincaré-Cartan forms in higher-order Calculus of Variations, in "Proc. of the Conference on Differential Geometry and its Applications, Nové Město na Moravě, Vol. II. Applications", Univerzita Karlova, Praga, 1984, pp. 61-91. (1984) Zbl0564.53013MR0793200
- V. N. Gusyatnikova A. M. Vinogradov V. A. Yumaguzhin, Secondary differential operators, J. Geom. Phys. 2 (1985), 23-65. (1985) MR0845467
- M. Henneaux, Equations of motions, commutation relations and ambiguities in the Lagrangian formalism, Ann. Phys. 140 (1982), 45-64. (1982) MR0660925
- M. Henneaux, L. C. Shepley, Lagrangians for spherically symmetric potentials, J. Math. Phys. 23 (1982), 2101-2104. (1982) Zbl0507.70022MR0680007
- M. Henneaux, On the inverse problem of the calculus of variations in field theory, J. Phys. A: Math. Gen. 17 (1984), 75-85. (1984) Zbl0557.70019MR0734109
- S. Hojman, H. Harleston, Equivalent Lagrangians: Multidimensional case, J. Math. Physics 22 (1981), 1414-1419. (1981) Zbl0522.70024MR0626131
- G. W. Horndeski, Differential operators associated with the Euler-Lagrange operator, Tensor 28 (1974), 303-318. (1974) Zbl0289.49045MR0356143
- J. Klein, Geometry of sprays. Lagrangian case. Principle of least curvature., in "Proc. IUTAM-ISIMM Symposium on Modern Developments in Analytical Mechanics, Vol. 1", (Benenti, Francavigilia, Lichnerowicz, eds.), Atti dela Accademia delle Scienze di Torino, 1983, pp. 177-196. (1983) Zbl0566.58012MR0773487
- I. Kolář, A geometrical version of the higher order Hamilton formalism in fibered manifolds, J. Geom. Phys. 1 (1984), 127-137. (1984) MR0794983
- L. Littlejohn, On the classification of differential equations having orthogonal polynomial solutions, Annali di Mathematica pure ed applicata 138 (1984), 35-53. (1984) Zbl0571.34003MR0779537
- D. Lovelock, The Einstein tensor and its generalizations, J. Math. Physics 12 (1971), 498-501. (1971) Zbl0213.48801MR0275835
- J. M. Masqué, Poincaré-Cartan forms in higher order variational calculus on fibred manifolds, Revista Matematica Iberoamericana 1 (1985), 85-126. (1985) MR0850411
- P. J. Olver, Applications of Lie Groups to Differential Equations, Springer-Verlag, New York, 1986. (1986) Zbl0588.22001MR0836734
- P. J. Olver, Darboux's theorem for Hamiltonian differential operators, (to appear).
- H. Rund, A Cartan form for the field theory of Carathéodory in the calculus of variations, in "Lecture Notes in Pure and Applied Mathematics No. 100: Differential Geometry, Calculus of Variations, and Their Applications", G. M. Rassias and T. M. Rassias (eds), Marcel Dekker, New York, 1985, pp. 455-470. (1985) Zbl0578.49025MR0822534
- W. Sarlet, Symmetries and alternative Lagrangians in higher-order mechanics, Phys. Lett. A 108 (1985), 14-18. (1985) MR0786789
- W. Sarlet F. Cantrijin, M. Crampin, A new look at second-order equations and Lagrangian mechanics, J. Phys. A: Math. Gen. 17 (1984), 1999-2009. (1984) MR0763792
- F. Takens, Symmetries, conservation laws and variational principles, in "Lecture Notes in Mathematics No. 597", Springer-Verlag, New York, 1977, pp. 581-603. (1977) Zbl0368.49019MR0650304
- F. Takens, A global version of the inverse problem to the calculus of variations, J. Diff. Geom. 14 (1979), 543-562. (1979) MR0600611
- G. Thompson, Second order equation fields and the inverse problem of Lagrangian dynamics, (to appear). Zbl0638.70013MR0917639
- E. Tonti, Inverse problem: Its general solution, in "Lecture Notes in Pure and Applied Mathematics No. 100: Differential Geometry, Calculus of Variations and Their Applications", Marcel Decker, New York, 1985, pp. 497-510. (1985) Zbl0583.49010MR0822537
- T. Tsujishita, On variation bicomplexes associated to differential equations, Osaka J. Math. 19 (1982), 311-363. (1982) Zbl0524.58041MR0667492
- W. M. Tulczyjew, The Euler-Lagrange resolution, in "Lecture Notes in Mathematics No. 836," Springer-Verlag, New York, 1980, pp. 22-48. (1980) Zbl0456.58012MR0607685
- A. M. Vinogradov, On the algebra-geometric foundation of Lagrangian field theory, Sov. Math. Dokl. 18 (1977), 1200-1204. (1977)
- A. M. Vinogradov, The C-spectral sequence, Lagrangian formalism and conservation laws I, II, J. Math. Anal. Appl. 100 (1984), 1-129. (1984) MR0739952
- E. Witten, Global aspects of current algebra, Nucl. Phys. B223 (1983), 422-432. (1983) MR0717915
Citations in EuDML Documents
top- Jan Chrastina, Solution of the inverse problem of the calculus of variations
- Joseph Grifone, Zoltán Muzsnay, Sur le problème inverse du calcul des variations : existence de lagrangiens associés à un spray dans le cas isotrope
- D. Opris, I. D. Albu, Geometrical aspects of the covariant dynamics of higher order
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.