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Abstract: We consider the problem of integrability of the Poisson equations describingspatial motion of a rigid body in the classical nonholonomic Suslov problem. Weobtain necessary conditions for their solutions to be meromorphic and show thatunder some further restrictions these conditions are also sufficient. Thelatter lead to a family of explicit meromorphic solutions, which correspond torather special motions of the body in space. We also give explicit extrapolynomial integrals in this case.In the more general case but under one restriction, the Poisson equationsare transformed into a generalized third order hypergeometric equation. A studyof its monodromy group allows us also to calculate the -scattering- angle: theangle between the axes of limit permanent rotations of the body in space.



Autor: Yuri Fedorov, Andrzej J. Maciejewski, Maria Przybylska

Fuente: https://arxiv.org/



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