Geodesic
The Liouville classification of integrable systems of the Clebsch case
Sbornik. Mathematics, Tome 193 (2002) no. 10, pp. 1507-1533 Cet article a éte moissonné depuis la source Math-Net.Ru

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The Fomenko–Zieschang invariants for the integrable Clebsch case in the dynamics of a rigid body are calculated. Thus a complete description of the structure of the Liouville foliations on isoenergy surfaces of this integrable Hamiltonian system is obtained. As a corollary the Liouville equivalence of the Euler and Clebsch cases for certain values of the parameters is established. 
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P. V. Morozov. The Liouville classification of integrable systems of the Clebsch case. Sbornik. Mathematics, Tome 193 (2002) no. 10, pp. 1507-1533. http://geodesic.mathdoc.fr/item/SM_2002_193_10_a5/

[1] Kirchhoff G. R., “Über die Bewegung eines Rotationskörpers in einer Flüssigkeit”, Crelle, 71 (1869), 237–262

[2] Clebsch A., “Über die Bewegung eines Körpers in einer Flüssigkeit”, Math. Ann., 3 (1871), 238–262 | DOI | MR

[3] Steklov V. A., O dvizhenii tyazhelogo tverdogo tela v zhidkosti, Kharkov, 1983 | Zbl

[4] Lyapunov A. M., “Novyi sluchai integriruemosti uravnenii dvizheniya tverdogo tela v zhidkosti”, Sobranie sochinenii, T. 1, Izd-vo AN SSSR, M., 1954, 320–324

[5] Chaplygin S. A., “O nekotorykh sluchayakh dvizheniya tverdogo tela v zhidkosti. 1; 2”, Polnoe sobranie sochinenii, T. 1, Izd-vo AN SSSR, L., 1933, 3–132

[6] Chaplygin S. A., “Novoe chastnoe reshenie zadachi o dvizhenii tverdogo tela v zhidkosti”, Polnoe sobranie sochinenii, T. 1, Izd-vo AN SSSR, L., 1933, 133–152

[7] Kharlamova E. I., “O dvizhenii tverdogo tela vokrug nepodvizhnoi tochki v tsentralnom nyutonovskom pole sil”, Izv. SO AN SSSR, 1959, no. 6, 7–17 | Zbl

[8] Pogosyan T. I., Kharlamov M. P., “Bifurkatsionnoe mnozhestvo i integralnye mnogoobraziya zadachi o dvizhenii tverdogo tela v lineinom pole sil”, PMM, 43 (1979), 419–428 | MR | Zbl

[9] Kharlamov M. P., “Fazovaya topologiya odnogo integriruemogo sluchaya dvizheniya tverdogo tela”, Mekhanika tverdogo tela, no. 11, Naukova dumka, Kiev, 1979, 50–63 | MR

[10] Pogosyan T. I., “Postroenie bifurkatsionnykh mnozhestv v odnoi zadache dinamiki tverdogo tela”, Mekhanika tverdogo tela, no. 12, Naukova dumka, Kiev, 1980, 3–23

[11] Pogosyan T. I., “Oblasti vozmozhnosti dvizheniya v zadache Klebsha. Kriticheskii sluchai”, Mekhanika tverdogo tela, no. 16, Naukova dumka, Kiev, 1983, 19–24 | MR

[12] Bolsinov A. V., Fomenko A. T., Integriruemye gamiltonovy sistemy. Geometriya. Topologiya. Klassifikatsiya, T. 1, 2, Izdatelskii dom “Udmurtskii universitet”, Izhevsk, 1999 | MR | Zbl

[13] Bolsinov A. V., Fomenko A. T., Vvedenie v topologiyu integriruemykh gamiltonovykh sistem, Nauka, M., 1997 | MR

[14] Oshemkov A. A., “Opisanie izoenergeticheskikh poverkhnostei integriruemykh gamiltonovykh sistem s dvumya stepenyami svobody”, Trudy seminara po vektornomu i tenzornomu analizu, no. 23, MGU, M., 1988, 122–132 | MR

[15] Oshemkov A. A., “Vychislenie invariantov Fomenko dlya osnovnykh integriruemykh sluchaev dinamiki tverdogo tela”, Trudy seminara po vektornomu i tenzornomu analizu, chast 2, no. 25, MGU, M., 1993, 23–109

[16] Lamb G., Gidrodinamika, GITTL, M.–L., 1947

[17] Magnus K., Giroskop. Teoriya i primenenie, Nauka, M., 1973

[18] Kozlov V. V., Simmetrii, topologiya i rezonansy v gamiltonovoi mekhanike, Izd-vo UdGU, Izhevsk, 1995 | MR | Zbl

[19] Novikov S. P., Shmeltser I., “Periodicheskie resheniya uravnenii Kirkhgofa svobodnogo dvizheniya tverdogo tela v idealnoi neszhimaemoi zhidkosti i rasshirennaya teoriya Lyusterika–Shnirelmana–Morsa (LMSh)”, Funkts. analiz i ego prilozh., 15:3 (1982), 54–66 | MR | Zbl

[20] Kharlamov M. P., Topologicheskii analiz integriruemykh zadach v dinamike tverdogo tela, Izd-vo LGU, L., 1988

[21] Bolsinov A. V., Rikhter P., Fomenko A. T., “Metod krugovykh molekul i topologiya volchka Kovalevskoi”, Matem. sb., 191:2 (2000), 3–42 | MR | Zbl

[22] Kalashnikov V. V. (ml.), “Ob ustoichivosti topologicheskoi struktury bottovskikh integriruemykh gamiltonovykh sistem s dvumya stepenyami svobody”, [12], T. 2, prilozhenie 2

[23] Kalashnikov V. V. (ml.), “Tipichnye integriruemye gamiltonovy sistemy na chetyrekhmernom simplekticheskom mnogoobrazii”, Izv. RAN. Ser. matem., 62:2 (1998), 49–74 | MR | Zbl

[24] Bolsinov A. V., Fomenko A. T., “Geodezicheskii potok ellipsoida traektorno ekvivalenten integriruemomu sluchayu Eilera v dinamike tverdogo tela”, Dokl. RAN, 339:3 (1994), 253–296 | MR | Zbl