Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics]
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Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics], 2010, Volume 6, Number 4, Pages 769–805 (Mi nd5)  

This article is cited in 17 scientific papers (total in 17 papers)

Topological analysis and Boolean functions. I. Methods and application to classical systems

M. P. Kharlamov

Volgograd Academy of Public Administration
References:
Abstract: We aim to completely formalize the rough topological analysis of integrable Hamiltonian systems admitting analytical solutions such that the initial phase variables along with the time derivatives of the auxiliary variables are expressed as rational functions (in fact, as polynomials) in some set of radicals depending on one variable each. We suggest a method to define the admissible regions in the integral constants space, the segments of oscillation of the separated variables and the number of connected components of integral manifolds and critical integral surfaces. This method is based on some algorithms of processing the tables of some Boolean vector-functions and of reducing the matrices of linear Boolean vector-functions to some canonical form. From this point of view we consider here the topologically richest classical problems of the rigid body dynamics. The article will be continued with the investigation of some new integrable problems.
Keywords: algebraic separation of variables, integral manifolds, Boolean functions, topological analysis, algorithms.
Received: 27.05.2010
Document Type: Article
UDC: 517.938.5:531.38+519.6
MSC: 70E17, 70G40
Language: Russian
Citation: M. P. Kharlamov, “Topological analysis and Boolean functions. I. Methods and application to classical systems”, Nelin. Dinam., 6:4 (2010), 769–805
Citation in format AMSBIB
\Bibitem{Kha10}
\by M.~P.~Kharlamov
\paper Topological analysis and Boolean functions. I.~Methods and application to classical systems
\jour Nelin. Dinam.
\yr 2010
\vol 6
\issue 4
\pages 769--805
\mathnet{http://mi.mathnet.ru/nd5}
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  • https://www.mathnet.ru/eng/nd/v6/i4/p769
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    This publication is cited in the following 17 articles:
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