Geodesic
New case of complete integrability of dynamics equations on a tangent fibering to a $3\mathrm{D}$ sphere
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2015), pp. 11-14 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper presents the results of study of the motion equations for a dynamically symmetric 4D-rigid body placed in a certain non-conservative field of forces. The form of the field is taken from the dynamics of actual 2D- and 3D-rigid bodies interacting with the medium in the case when the system contains a non-conservative pair of forces forcing the center of mass of a body to move rectilinearly and uniformly. A new case of integrability is obtained for dynamic equations of body motion in a resisting medium filling a four-dimensional space under presence of a tracking force. 
@article{VMUMM_2015_3_a1,
     author = {M. V. Shamolin},
     title = {New case of complete integrability of dynamics equations on a tangent fibering to a $3\mathrm{D}$ sphere},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {11--14},
     year = {2015},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2015_3_a1/}
}
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M. V. Shamolin. New case of complete integrability of dynamics equations on a tangent fibering to a $3\mathrm{D}$ sphere. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2015), pp. 11-14. http://geodesic.mathdoc.fr/item/VMUMM_2015_3_a1/

[1] Shamolin M.V., Metody analiza dinamicheskikh sistem s peremennoi dissipatsiei v dinamike tverdogo tela, Ekzamen, M., 2007

[2] Shamolin M.V., “Integriruemost po Yakobi v zadache o dvizhenii chetyrekhmernogo tverdogo tela v soprotivlyayuscheisya srede”, Dokl. RAN, 375:3 (2000), 343–346

[3] Shamolin M.V., “Ob integriruemosti v transtsendentnykh funktsiyakh”, Uspekhi matem. nauk, 53:3 (1998), 209–210 | DOI | MR | Zbl

[4] Bogoyavlenskii O.I., “Nekotorye integriruemye sluchai uravnenii Eilera”, Dokl. AN SSSR, 287:5 (1986), 1105–1108 | MR

[5] Bogoyavlenskii O.I., “Dinamika tverdogo tela s $n$ ellipsoidalnymi polostyami, zapolnennymi magnitnoi zhidkostyu”, Dokl. AN SSSR, 272:6 (1983), 1364–1367 | MR

[6] Veselov A.P., “Uravnenie Landau–Lifshitsa i integriruemye sistemy klassicheskoi mekhaniki”, Dokl. AN SSSR, 270:5 (1983), 1094–1097 | MR

[7] Veselov A.P., “Ob usloviyakh integriruemosti uravnenii Eilera na ${\rm so}(4)$”, Dokl. AN SSSR, 270:6 (1983), 1298–1300 | MR | Zbl

[8] Manakov S.V., “Zamechanie ob integrirovanii uravnenii Eilera dinamiki $n$-mernogo tverdogo tela”, Funkts. analiz i ego pril., 10:4 (1976), 93–94 | MR | Zbl