On a class of forced nonlinear oscillators at resonance
On a deformed version of the two-disk dynamo system
We give some deformations of the Rikitake two-disk dynamo system. Particularly, we consider an integrable deformation of an integrable version of the Rikitake system. The deformed system is a three-dimensional Hamilton-Poisson system. We present two Lie-Poisson structures and also symplectic realizations. Furthermore, we give a prequantization result of one of the Poisson manifold. We study the stability of the equilibrium states and we prove the existence of periodic orbits. We analyze some properties...
On Lyapunov stability/instability of equilibria of free damped pendulum with periodically oscillating suspension point
We discuss Lyapunov stability/instability of both lower and upper equilibria of free damped pendulum with periodically oscillating suspension point. We recall the results of Bogolyubov and Kapitza, provide new effective criteria of stability/instability of the equilibria of pendulum equation, and give the exact and complete proofs. The criteria obtained are formulated in terms of positivity/negativity of Green's functions of the periodic boundary value problems for linearized equations. Furthermore,...
On nonlinear stability of polytropic galaxies
On stability problem of a top
On the asymptotic behavior for a damped oscillator under a sublinear friction.
Mostramos la existencia de dos curvas de datos iniciales (x0, v0) para las cuales las soluciones x(t) correspondientes del problema de Cauchy asociado a la ecuación xtt + |xt|α-1 xt + x = 0, supuesto α ∈ (0,1), se anulan idénticamente después de un tiempo finito. Mediante métodos asintóticos y argumentos de comparación mostramos que para muchos otros datos iniciales las soluciones decaen a 0, en un tiempo infinito, como t-α / (1-α).
On the dynamics of a nonlinear multidimensional oscillator with memory.
On the evection resonance and its connection to the stability of outer satellites.
On the problem of stability for near to integrable Hamiltonian systems.
On the state observation and stability for uncertain nonlinear systems
In this paper, we treat the class of nonlinear uncertain dynamic systems that was considered in [3,2,1,4]. We consider continuous-time dynamical systems whose nominal part is linear and whose uncertain part is norm-bounded. We study the problems of state observation and obtaining stabilizing controller for uncertain nonlinear systems, where the uncertainties are characterized by known bounds.
Oscillateurs harmoniques faiblement perturbés : l'algorithme numérique des «pas de géants»
Oscillation susceptibility analysis of the ADMIRE aircraft along the path of longitudinal flight equilibriums in two different mathematical models.
Oscillations de systèmes hamiltoniens non linéaires. III
Oscillations presque-périodiques forcées d'équations d'Euler-Lagrange