标题： 非完整Suslov问题中的泊松方程：可积性，亚纯解和超几何解 显示英文标题

标题： The Poisson equations in the nonholonomic Suslov problem: Integrability, meromorphic and hypergeometric solutions

摘要： 我们考虑经典非完整Suslov问题中刚体空间运动的Poisson方程的可积性问题。 我们得到了其解为亚纯的必要条件，并表明在一些进一步限制下这些条件也是充分的。 后者导致了一族显式的亚纯解，这些解对应于物体在空间中的相当特殊的运动。 我们还给出了这种情况下的显式额外多项式积分。 在更一般的情况下（但有一个限制），Poisson方程被转化为一个广义的三阶超几何方程。 对其单值群的研究也使我们能够计算“散射”角：物体在空间中极限定常旋转轴之间的角度。 显示英文摘要

摘要： We consider the problem of integrability of the Poisson equations describing spatial motion of a rigid body in the classical nonholonomic Suslov problem. We obtain necessary conditions for their solutions to be meromorphic and show that under some further restrictions these conditions are also sufficient. The latter lead to a family of explicit meromorphic solutions, which correspond to rather special motions of the body in space. We also give explicit extra polynomial integrals in this case. In the more general case (but under one restriction), the Poisson equations are transformed into a generalized third order hypergeometric equation. A study of its monodromy group allows us also to calculate the "scattering" angle: the angle between the axes of limit permanent rotations of the body in space.