Related papers: Vibrations of a Pendulum with Oscillating Support …
Dynamics of a matter wave soliton bouncing on the reflecting surface (atomic mirror) under the effect of gravity has been studied by analytical and numerical means. The analytical description is based on the variational approach. Resonant…
We present a continuation method that enables one to track or continue branches of periodic orbits directly in an experiment when a parameter is changed. A control-based setup in combination with Newton iterations ensures that the periodic…
An experimental study of bifurcations associated with stability of stationary points (SP's) in a parametrically forced magnetic pendulum and a comparison of its results with numerical results are presented. The critical values for which the…
The dynamics of a non-autonomous oscillator in which the phase and frequency of the external force depend on the dynamical variable is studied. Such a control of the phase and frequency of the external force leads to the appearance of…
In this paper, the general perturbation problem of piecewise smooth integrable differential systems with two switching planes is considered. Firstly, when the unperturbed system has a family of periodic orbits, the first order Melnikov…
In this paper we deal with the care one must have in adopting approximations in regard with terms he chooses to leave behind in the particular case of the expression valid for the maximum period of a long pendulum oscillating near Earth's…
An elastic double pendulum subject to a force acting along a fixed straight line, the so-called "Reut's column problem", is a structure exhibiting flutter and divergence instability, which was never realized in practice and thus debated…
The inverted pendulum is a mechanical system with a rapidly oscillating pivot point. Using techniques similar in spirit to the methodology of effective field theories, we derive an effective Lagrangian that allows for the systematic…
An exact expression for the determinant of the splitting matrix is derived: it allows us to analyze the asympotic behaviour needed to amend the large angles theorem proposed in Ann. Inst. H. Poincar\'e, B-60, 1, 1994. The asymptotic…
We argue that the motion of vacancies in a pinned vortex lattice may dominate the contribution to the Hall effect in an appropriate parameter regime for a superconductor. Based on this consideration a model is constructed to explain the…
We provide sufficient conditions for the existence of periodic solutions with small amplitude of the non--linear planar double pendulum perturbed by smooth or non--smooth functions.
The observed long-term spin-down evolution of isolated radio pulsars cannot be explained by the standard magnetic dipole radiation with a constant braking torque. However how and why the torque varies still remains controversial, which is…
We use the Melnikov integral method to prove that the Hamiltonian flow on the zero-energy manifold for the Kepler problem perturbed by a quadrupole moment is chaotic, irrespective of the perturbation being of prolate or oblate type. This…
We present a Melnikov method to analyze two-dimensional stable or unstable manifolds associated with a saddle point in three-dimensional non-volume preserving autonomous systems. The time-varying perturbed locations of such manifolds is…
We review the dynamical behavior of giant fluid vesicles in various types of external hydrodynamic flow. The interplay between stresses arising from membrane elasticity, hydrodynamic flows, and the ever present thermal fluctuations leads to…
The complete explicitly covariant 4-dimensional description of the dynamics of a free classical particle with spin within the framework of the special relativity theory is presented. The key point of our approach is the the introduction of…
We show asymptotic, exponential stability of the equilibrium configuration, $\smallL$, of a hollow physical pendulum with its inner part entirely filled with a viscous liquid, corresponding to the center of mass being in the lowest…
We apply KAM theory to the equation of the forced relativistic pendulum to prove that all the solutions have bounded momentum. Subsequently, we detect the existence of quasiperiodic solutions in a generalized sense. This is achieved using a…
A new type of instability resulting in oscillatory propagating kinks is presented. It is observed in periodically forced oscillatory media at 1:1 resonance, where phase kinks have close similarities to pulses in excitable media. Considering…
Particle sedimentation in the vicinity of a fixed horizontal vortex with time-dependent intensity can be chaotic, provided gravity is sufficient to displace the particle cloud while the vortex is off or weak. This "stretch, sediment and…