Geodesic
An extended Hamilton--Jacobi method
Russian journal of nonlinear dynamics, Tome 8 (2012) no. 3, pp. 549-568.

Voir la notice de l'article provenant de la source Math-Net.Ru

We develop a new method for solving Hamilton’s canonical differential equations. The method is based on the search of invariant vortex manifolds of special type. In the case of Lagrangian (potential) manifolds, we arrive at the classical Hamilton–Jacobi method.
Keywords: generalized Lamb's equations, vortex manifolds, Clebsch potentials, Lagrange brackets. 
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Valery V. Kozlov. An extended Hamilton--Jacobi method. Russian journal of nonlinear dynamics, Tome 8 (2012) no. 3, pp. 549-568. http://geodesic.mathdoc.fr/item/ND_2012_8_3_a9/

[1] Kozlov V. V., Obschaya teoriya vikhrei, UdGU, Izhevsk, 1998, 238 pp. | MR

[2] Uitteker E. T., Analiticheskaya dinamika, Gostekhizdat, M.–L., 1937, 500 pp.

[3] Birkgof Dzh. D., Dinamicheskie sistemy, Gostekhizdat, M.–L., 1941, 320 pp.

[4] Santilli R. M., Foundations of theoretical mechanics, v. 2, Birkhoffian generalization of Hamiltonian mechanics, Springer, New York–Berlin, 1983, 370 pp. | MR | Zbl

[5] Kozlov V. V., “Ob invariantnykh mnogoobraziyakh uravnenii Gamiltona”, PMM, 76:4 (2012), 528–541 | MR

[6] Kartan E., Integralnye invarianty, Gostekhizdat, M.–L., 1940, 216 pp.

[7] Arnold V. I., Kozlov V. V., Neishtadt A. I., Matematicheskie aspekty klassicheskoi i nebesnoi mekhaniki, Editorial URSS, M., 2002, 416 pp. | Zbl

[8] Nekhoroshev N. N., “Peremennye deistvie–ugol i ikh obobscheniya”, Tr. Mosk. matem. obsch-va, 26, 1972, 181–198 | Zbl

[9] Stekloff W., “Sur une généralisation d'un théoreme de Jacobi”, C. R. Acad. Sci. Paris, 148 (1909), 153–155

[10] Stekloff W., “Application d'un théorème généralisé de Jacobi au problème de S. Lie–Mayer”, C. R. Acad. Sci. Paris, 148 (1909), 277–279 | Zbl

[11] Stekloff W., “Application du théorème généralisé de Jacobi au problème de Jacobi–Lie”, C. R. Acad. Sci. Paris, 148 (1909), 465–468 | Zbl

[12] Steklov V. A., Raboty po mekhanike 1902–1909 gg., Perevody s frantsuzskogo, Institut kompyuternykh issledovanii, M.–Izhevsk, 2011, 492 pp.

[13] Mischenko A. S., Fomenko A. T., “Obobschennyi metod Liuvillya integrirovaniya gamiltonovykh sistem”, Funkts. analiz i ego pril., 12:2 (1978), 46–56 | MR

[14] Li S., Teoriya grupp preobrazovanii, V 3-kh chastyakh, v. 2, Institut kompyuternykh issledovanii, M.–Izhevsk, 2012, 640 pp.

[15] Brailov A. V., “Polnaya integriruemost nekotorykh geodezicheskikh potokov i integriruemye sistemy s nekommutiruyuschimi integralami”, Dokl. AN SSSR, 271:2 (1983), 273–276 | MR