CERTAIN CONDITIONS OF INTEGRABILITY OF DYNAMICAL SYSTEMS IN TRANSCENDENTAL FUNCTIONS
- Authors: Pokhodnya N.1, Shamolin M.2
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Affiliations:
- Sholokhov Moscow State University for the Humanities
- Moscow State University
- Issue: Vol 19, No 9.1 (2013)
- Pages: 35-41
- Section: Articles
- URL: https://journals.ssau.ru/est/article/view/4684
- DOI: https://doi.org/10.18287/2541-7525-2013-19-9.1-35-41
- ID: 4684
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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