Qualitative Analysis of a Dynamical System with Irrational First Integrals
We conduct qualitative analysis for a completely integrable system of differential equations with irrational first integrals. These equations originate from gas dynamics and describe adiabatical motions of a compressible gas cloud with homogeneous deformation. We study the mechanical analog of this gas dynamical system – the rotational motion of a spheroidal rigid body around a fixed point in a potential force field described by an irrational function. Within our study, equilibria, pendulum oscillations and invariant manifolds, which these solutions belong to, have been found. The sufficient conditions of their stability in Lyapunov’s sense have been derived and compared with the necessary ones. The analysis has been performed with the aid of computer algebra tools which proved to be essential. The computer algebra system “Mathematica” was employed.
This work was supported by the Russian Foundation for Basic Research (Project 16-07-00201a) and the Program for the Leading Scientific Schools of the Russian Federation (NSh-8081.2016.9).
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