Open AccessCERTAIN CONDITIONS OF INTEGRABILITY OF DYNAMICAL SYSTEMS IN TRANSCENDENTAL FUNCTIONS
Author(s) -
N.V. Pokhodnya,
М. В. Шамолин
Publication year - 2013
Publication title -
vestnik samarskogo universiteta. estestvennonaučnaâ seriâ
Language(s) - English
Resource type - Journals
eISSN - 2712-8954
pISSN - 2541-7525
DOI - 10.18287/2541-7525-2013-19-9.1-35-41
Subject(s) - tangent bundle , mathematics , tangent , dynamical systems theory , motion (physics) , pendulum , elementary function , mathematical analysis , flow (mathematics) , parametric statistics , double pendulum , dynamical system (definition) , pure mathematics , classical mechanics , physics , geometry , tangent space , inverted pendulum , nonlinear system , statistics , quantum mechanics
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.