Geodesic
New case of integrability in dynamics of multi-dimensional body
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 9 (2012), pp. 136-150 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this chapter the new results are systematized on study of the equations of motion of dynamically symmetrical four-dimensional ($4D-$) rigid body which residing in a certain nonconservative field of forces in case of special dynamical symmetry. Its type is unoriginal from dynamics of the real smaller-dimensional rigid bodies of interacting with a resisting medium on the laws of a jet flow, under which the nonconservative tracing force acts onto the body and forces both the value of velocity of a certain typical point of the rigid body and the certain phase variable to remain as constant in all time, that means the presence in system nonintegrable servo-constraints.
Keywords: multi-dimensional rigid body, integrability, transcendental first integral. 
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N. V. Pokhodnya; M. V. Shamolin. New case of integrability in dynamics of multi-dimensional body. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 9 (2012), pp. 136-150. http://geodesic.mathdoc.fr/item/VSGU_2012_9_a13/

[1] Shamolin M. V., Metody analiza dinamicheskikh sistem s peremennoi dissipatsiei v dinamike tverdogo tela, Ekzamen, M., 2007, 352 pp.

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

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

[4] Chaplygin S. A., “O dvizhenii tyazhelykh tel v neszhimaemoi zhidkosti”, Poln. sobr. soch., v. 1, Izd-vo AN SSSR, L., 1933, 133–135