This article is cited in 2 papers

Nonholonomic mechanics

Hirota–Kimura Type Discretization of the Classical Nonholonomic Suslov Problem

V. Dragović^ab, B. Gajić<sup>a

a</sup> Mathematical Institute SANU, Kneza Mihaila 36, Belgrade, Serbia
^b Grupo de Fisica Matematica, Complexo Interdisciplinar da Universidade de Lisboa, Av. Prof. Gama Pinto, 2, PT-1649-003 Lisboa, Portugal

Abstract: 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.

Keywords: Hirota–Kimura type discretization, nonholonomic mechanics, Suslov problem, rigid body.

MSC: 37J60, 70H06

Received: 26.06.2008
Accepted: 14.07.2008

Language: English

DOI: 10.1134/S1560354708040023

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