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Эта публикация цитируется в 9 научных статьях (всего в 9 статьях)
Mathematical problems of nonlinearity
Vibrational Stability of Periodic Solutions of the Liouville Equations
E. V. Vetchanina, E. A. Mikishaninab a Udmurt State University,
ul. Universitetskaya 1, Izhevsk, 426034 Russia
b Chuvash State University,
Moskovskii prosp. 15, Cheboksary, 428015 Russia
Аннотация:
The dynamics of a body with a fixed point, variable moments of inertia and internal rotors are considered. A stability analysis of permanent rotations and periodic solutions of the system is carried out. In some simplest cases the stability analysis is reduced to investigating the stability of the zero solution of Hill’s equation. It is shown that by periodically changing the moments of inertia it is possible to stabilize unstable permanent rotations of the system. In addition, stable dynamical regimes can lose stability due to a parametric resonance. It is shown that, as the oscillation frequency of the moments of inertia increases, the dynamics of the system becomes close to an integrable one.
Ключевые слова:
Liouville equations, Euler – Poisson equations, Hill’s equation, Mathieu equation, parametric resonance, vibrostabilization, Euler – Poinsot case, Joukowski – Volterra case.
Поступила в редакцию: 17.07.2019 Принята в печать: 23.09.2019
Образец цитирования:
E. V. Vetchanin, E. A. Mikishanina, “Vibrational Stability of Periodic Solutions of the Liouville Equations”, Rus. J. Nonlin. Dyn., 15:3 (2019), 351–363
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/nd665 https://www.mathnet.ru/rus/nd/v15/i3/p351
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