Abstract:
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.
Citation:
E. V. Vetchanin, E. A. Mikishanina, “Vibrational Stability of Periodic Solutions of the Liouville Equations”, Rus. J. Nonlin. Dyn., 15:3 (2019), 351–363
\Bibitem{VetMik19}
\by E. V. Vetchanin, E. A. Mikishanina
\paper Vibrational Stability of Periodic Solutions of the Liouville Equations
\jour Rus. J. Nonlin. Dyn.
\yr 2019
\vol 15
\issue 3
\pages 351--363
\mathnet{http://mi.mathnet.ru/nd665}
\crossref{https://doi.org/10.20537/nd190312}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4021375}
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https://www.mathnet.ru/eng/nd665
https://www.mathnet.ru/eng/nd/v15/i3/p351
This publication is cited in the following 9 articles:
E. M. Artemova, A. A. Kilin, Yu. V. Korobeinikova, “Issledovanie orbitalnoi ustoichivosti pryamolineinykh kachenii roller-reisera po vibriruyuschei ploskosti”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 32:4 (2022), 615–629
E. V. Vetchanin, I. S. Mamaev, “Chislennyi analiz periodicheskikh upravlenii vodnogo robota neizmennoi formy”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 32:4 (2022), 644–660
W.-Sh. Du, M. Kostic, M. Pinto, “Almost periodic functions and their applications: a survey of results and perspectives”, J. Math., 2021 (2021)
Evgeny V. Vetchanin, 2021 International Conference “Nonlinearity, Information and Robotics” (NIR), 2021, 1
Alexander Kilin, Elena Pivovarova, 2021 International Conference “Nonlinearity, Information and Robotics” (NIR), 2021, 1
I. S. Mamaev, E. V. Vetchanin, “Dynamics of Rubber Chaplygin Sphere Under Periodic Control”, Regul. Chaotic Dyn., 25:2 (2020), 215–236
A. A. Kilin, E. N. Pivovarova, “Nonintegrability of the Problem of a Spherical TOP Rolling on a Vibrating Plane”, Vestn. Udmurt. Univ.-Mat. Mekh. Kompyuternye Nauk., 30:4 (2020), 628–644
Evgeny V. Vetchanin, 2020 International Conference Nonlinearity, Information and Robotics (NIR), 2020, 1
Ivan S. Mamaev, Evgeny V. Vetchanin, 2020 International Conference Nonlinearity, Information and Robotics (NIR), 2020, 1
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