Related papers: Remarks on forced oscillations in some systems wit…
We present sufficient conditions for the existence of forced oscillations in non-autonomous mechanical systems. Previously, similar results were obtained for systems with friction. Presented results hold both for systems with and without…
Consider a periodically forced nonlinear system which can be presented as a collection of smaller subsystems with pairwise interactions between them. Each subsystem is assumed to be a massive point moving with friction on a compact surface,…
We present sufficient conditions for the existence of a periodic solution for a class of systems describing the periodically forced motion of a massive point on a compact surface with a boundary.
We consider the forced motion of a relativistic particle constrained on a curve and present sufficient conditions for periodic oscillations by means of an illustrative geometrical approach. Obtained result is illustrated by a few examples…
We study forced oscillations of a rod with a body attached to its free end so that the motion of a system is described by two sets of equations, one of integer and the other of the fractional order. To the constitutive equation we associate…
Forced oscillation of a system composed of two pendulums coupled by a spring in the presence of damping is investigated. In the steady state and within the small angle approximation we solve the system equations of motion and obtain the…
We study two type effects of gravitational field on mechanical gyroscopes (i.e. rotating extended bodies). The first depends on special relativity and equivalence principle. The second is related to the coupling (i.e. a new force) between…
The oscillation periods bounded by a simple pendulum and an oscillating rigid rod are illustrated using a multiple pendulum. Oscillation periods between these two limits are obtained. A theoretical approach using the Lagrangian formalism…
A model for a possible variable cosmic object is presented. The model consists of a massive shell surrounding a compact object. The gravitational and self-gravitational forces tend to collapse the shell, but the internal tangential stresses…
We relate Gaussian curvature to the gyroscopic force, thus giving a mechanical interpretation of the former and a geometrical interpretation of the latter. We do so by considering the motion of a spinning disk constrained to be tangent to a…
In the paper we consider systems in oscillating force fields such that the classical method of averaging can be applied. We present sufficient conditions for the existence of forced oscillations in such systems and study the asymptotic…
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…
The dynamics of force free motion of pendulums on surfaces of constant Gaussian curvature is addressed when the pivot moves along a geodesic obtaining the Lagragian of the system. As a application it is possible the study of elastic and…
Natural dynamos such as planets and stars generate global scale magnetic field despite the inferred presence of small scale turbulence. Such systems are known as large scale dynamos and are typically driven by convection and influenced by…
This study investigates the dynamics of a magnetic pendulum under time-varying magnetic excitation with a position-dependent phase. The system exhibits complex chaotic and regular dynamics, validated through simulations and experiments. The…
We propose a new mechanism of friction in resonantly driven vibrational systems. The form of the friction force follows from the time- and spatial-symmetry arguments. We consider a microscopic mechanism of this resonant force in…
We study non-resonant circles for strong magnetic fields on a closed, connected, oriented surface and show how these can be used to prove the existence of trapping regions and of periodic magnetic geodesics with prescribed low speed. As a…
Dynamo action in planetary cores has been extensively studied in the context of convectively-driven flows. We show in this letter that mechanical forcings, namely tides, libration and precession, are also able to kinematically sustain a…
We study the phenomenon of gyroscopic precession and the analogues of inertial forces within the framework of general relativity. Covariant connections between the two are established for circular orbits in stationary spacetimes with axial…
We analyse a mechanical system in two-dimensional relative motion with friction. Although the system is simple, the peculiar interplay between two kinetic friction forces and gravity leads to the wide range of admissible solutions exceeding…