经典非完整Suslov问题的Hirota-Kimura型离散化
Hirota-Kimura Type Discretization of the Classical Nonholonomic Suslov Problem
摘要：
对经典的非完整刚体运动的Suslov问题构造了Hirota-Kimura型离散。我们发现了第一积分证明了可积性。此外，我们已经表明，离散轨迹渐近倾向于所谓的稳态旋转的离散类比线。最后一个属性完全对应于连续Suslov情况下的著名属性。给出了解的显式表达式。在n维情况下，我们给出离散方程。
英文摘要：
We constructed Hirota-Kimura type discretization of the classical nonholonomic Suslov problem of motion of rigid body fixed at a point. We found a first integral proving integrability. Also, we have shown that discrete trajectories asymptotically tend to a line of discrete analogies of so-called steady-state rotations. The last property completely corresponds to well-known property of the continuous Suslov case. The explicite formulae for solutions are given. In n-dimensional case we give discrete equations.
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