Geodesic
New case of integrability in dynamics of multi-dimensional body
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 9 (2012), pp. 136-150

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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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     author = {N. V. Pokhodnya and M. V. Shamolin},
     title = {New case of integrability in dynamics of multi-dimensional body},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {136--150},
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     number = {9},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2012_9_a13/}
}
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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/