Hirota-Kimura Type Discretization of the Classical Nonholonomic Suslov Problem

Details Hirota-Kimura Type Discretization of the Classical Nonholonomic Suslov Problem Hirota-Kimura Type Discretization of the Classical Nonholonomic Suslov Problem

2008-07-18

arxiv.org/abs/0807.2966v1

Regular and Chaotic Dynamics, Vol. 13, No 4, (2008)

Physics

Mathematical Physics

10 pages, 4 pictures

Scientific paper

10.1134/S1560354708040023

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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