1.
Vetchanin E. V., Mikishanina E. A.
Vibrational Stability of Periodic Solutions of the Liouville Equations
Russian Journal of Nonlinear Dynamics, 2019, vol. 15, no. 3, pp. 351-363
Abstract
pdf (775.13 Kb)
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.
| Keywords: |
Liouville equations, Euler –Poisson equations, Hill’s equation, Mathieu equation, parametric resonance, vibrostabilization, Euler – Poinsot case, Joukowski –Volterra case |
| Citation: |
Vetchanin E. V., Mikishanina E. A., Vibrational Stability of Periodic Solutions of the Liouville Equations, Russian Journal of Nonlinear Dynamics, 2019, vol. 15, no. 3, pp. 351-363 |
| DOI: |
10.20537/nd190312 |
| Full text: |
pdf
(775.13 Kb)
|
Journal Info
| Impact-factor RSCI (2022): |
0.259 (Q3) |
| ISSN (print): |
2658-5324 |
| ISSN (online): |
2658-5316 |
| Site: |
http://nd.ics.org.ru/ |
