Integer lattices of action-angle variables for “spherical pendulum” system
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2014), pp. 6-17 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper we study the topology of a “spherical pendulum” system and construct the lattice generated by lines of integer levels of action variables for this system. We describe an algorithm for computing numerical marks of Fomenko–Zieschang invariant and monodromy matrices using these lattices. We apply this algorithm to a “spherical pendulum” system.
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     author = {E. O. Kantonistova},
     title = {Integer lattices of action-angle variables for {\textquotedblleft}spherical pendulum{\textquotedblright} system},
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     pages = {6--17},
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     url = {http://geodesic.mathdoc.fr/item/VMUMM_2014_4_a1/}
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E. O. Kantonistova. Integer lattices of action-angle variables for “spherical pendulum” system. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2014), pp. 6-17. http://geodesic.mathdoc.fr/item/VMUMM_2014_4_a1/

[1] Bolsinov A.V., Fomenko A.T., Integriruemye gamiltonovy sistemy, Izdatelskii dom “Udmurtskii universitet”, Izhevsk, 1999 | MR

[2] Fomenko A.T., “Teoriya Morsa integriruemykh gamiltonovykh sistem”, Dokl. AN SSSR, 287:5 (1986), 1071–1075 | MR | Zbl

[3] Fomenko A.T., Tsishang Kh., “O topologii trekhmernykh mnogoobrazii, voznikayuschikh v gamiltonovoi mekhanike”, Dokl. AN SSSR, 294:2 (1987), 283–287 | MR | Zbl

[4] Cushman R.H., Bates L.M., Global aspects of classical integrable systems, Birkhauser, Basel, 1997 | MR | Zbl

[5] Cushman R.H., Duistermaat J.J., “The quantum mechanical spherical pendulum”, Bull. Amer. Math. Soc. (N.S.), 19:2 (1988), 475–479 | DOI | MR | Zbl

[6] Pussen V., Lektsii po teoreticheskoi mekhanike, v. 2, IL, M., 1949

[7] Kantonistova E.O., “Tselochislennye reshetki peremennykh deistviya dlya obobschennogo sluchaya Lagranzha”, Vestn. Mosk. un-ta. Matem. Mekhan., 2012, no. 1, 54–58 | MR | Zbl