非完整Suslov问题中的Poisson方程：可积性、亚纯解和超几何解
The Poisson equations in the nonholonomic Suslov problem: Integrability, meromorphic and hypergeometric solutions
摘要：
考虑经典非完整Suslov问题中描述刚体空间运动的Poisson方程的可积性问题。我们得到了它们的解是亚纯解的必要条件，并证明了在进一步的限制下这些条件也是充分的。后者导致一族显式亚纯解，这对应于相当特殊的运动的身体在空间中。在这种情况下，我们也给出了显式的额外的多项式积分。在更一般的情况下（但在一个限制下），泊松方程转化为一个广义的三阶超几何方程。一个研究其monodromy组允许我们也计算“散射”角：轴之间的角度有限的永久旋转的身体在空间中。
英文摘要：
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.
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