Qualitative Analysis of a Dynamical System with Irrational First Integrals
Авторы: Irtegov V., Titorenko T.
Журнал: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Том: 11077 LNCS
Отчётный год: 2018
Аннотация: 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.
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