CERTAIN CONDITIONS OF INTEGRABILITY OF DYNAMICAL SYSTEMS IN TRANSCENDENTAL FUNCTIONS



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Abstract

Certain general conditions of integrability in elementary functions for the systems on the tangent bundle of two-dimensional sphere are studied. At that an interesting example of three-dimensional phase pattern of pendulum-like system which describes the motion of spherical pendulum, placed in an over-run medium flow. Sufficient conditions of existence of the first integrals expressed through the finite combination of elementary functions, for multi-parametric third order systems are presented.

About the authors

N.V. Pokhodnya

Sholokhov Moscow State University for the Humanities

Author for correspondence.
Email: morenov.sv@ssau.ru

M.V. Shamolin

Moscow State University

Email: morenov.sv@ssau.ru

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Copyright (c) 2013 Pokhodnya N., Shamolin M.

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