Hirota-Kimura type discretization of the classical nonholonomic Suslov problem
نویسندگان
چکیده
منابع مشابه
On the Hamiltonian Structure of Hirota-kimura Discretization of the Euler Top
This paper deals with a remarkable integrable discretization of the so(3) Euler top introduced by Hirota and Kimura. Such a discretization leads to an explicit map, whose integrability has been understood by finding two independent integrals of motion and a solution in terms of elliptic functions. Our goal is the construction of its Hamiltonian formulation. After giving a simplified and streaml...
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R. Hirota and K. Kimura discovered integrable discretizations of the Euler and the Lagrange tops, given by birational maps. Their method is a specialization to the integrable context of a general discretization scheme introduced by W. Kahan and applicable to any vector field with a quadratic dependence on phase variables. According to a proposal by T. Ratiu, discretizations of the Hirota-Kimura...
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15 صفحه اولThe Poisson equations in the nonholonomic Suslov problem: Integrability, meromorphic and hypergeometric solutions
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 ...
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ژورنال
عنوان ژورنال: Regular and Chaotic Dynamics
سال: 2008
ISSN: 1560-3547,1468-4845
DOI: 10.1134/s1560354708040023