Related papers: Oscillations bounded by the simple pendulum and th…
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…
A model of two oscillating pendula placed on a mobile support is studied. Once an overall scheme of equations, under general assumptions, is formulated via the Lagrangian equations of motion, the specific case of absence of escapement is…
We study dynamics of the inverted pendulum on the wheel on a soft surface and under a proportional-integral-derivative controller. The behaviour of such pendulum is modelled by a system with a differential inclusion. If the the system has a…
We obtain tight upper and lower bounds to the eigenvalues of an anharmonic oscillator with a rational potential. We compare our bounds with results given by other approaches.
We introduce a simple variational principle for coherent material vortices in two-dimensional turbulence. Vortex boundaries are sought as closed stationary curves of the averaged Lagrangian strain. Solutions to this problem turn out to be…
We consider a periodic problem for the motion of a charged particle in a magnetic field. Introducing a notion of Ricci curvature for such Lagrangian systems and using the methods of the calculus of variations in the large, we prove the…
In the present work, we study the classical behavior of an electric dipole in presence of an external uniform magnetic field. We derive equations and constants of motion from the Lagrangian formulation. We obtain an infinitely periodic…
In this survey, we present a geometric description of Lagrangian and Hamiltonian Mechanics on Lie algebroids. The flexibility of the Lie algebroid formalism allows us to analyze systems subject to nonholonomic constraints, mechanical…
The prepared doctoral dissertation focuses on studying dynamics of systems composed of magnetic pendulums subjected to a non-stationary magnetic field. A magnetic pendulum is a physical pendulum with a magnet attached to its end and is…
In this paper we provide a sufficient condition for the linear instability of a periodic orbit for a free period Lagrangian system on a Riemannian manifold. The main result establish a general criterion for the linear instability of a maybe…
In this paper, we consider rods whose thickness vary linearly between $\eps$ and $\eps^2$. Our aim is to study the asymptotic behavior of these rods in the framework of the linear elasticity. We use a decomposition method of the…
Classical description of relativistic pointlike particle with intrinsic degrees of freedom such as isospin or colour is proposed. It is based on the Lagrangian of general form defined on the tangent bundle over a principal fibre bundle. It…
The solutions that describe the motion of the classical simple pendulum have been known for very long time and are given in terms of elliptic functions, which are doubly periodic functions in the complex plane. The independent variable of…
The purpose of this paper is describe Lagrangian Mechanics for constrained systems on Lie algebroids, a natural framework which covers a wide range of situations (systems on Lie groups, quotients by the action of a Lie group, standard…
This contribution reports on numerical simulations of 2D granular flows on erodible beds. The broad aim is to investigate whether simple flows of model granular matter exhibits spontaneous oscillatory motion in generic flow conditions, and…
In this study, the properties of an oscillating system composed of a pendulum connected to a seesaw and placed on a moving platform with a certain slope are analyzed. Using complex numbers to collect the information contained in the system…
Longitudinal oscillations in prominences are common phenomena on the Sun. These oscillations can be used to infer the geometry and intensity of the filament magnetic field. Previous theoretical studies of longitudinal oscillations made two…
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…
This work is motivated by a desire to understand transitions between stable equilibria observed in Stommel's 1961 thermohaline circulation model. We adapt the model, including a forcing parameter as a dynamic slow variable. The resulting…
Oscillators and rotators are among the most important physical systems. For centuries the only known rotating systems that actually reached the limits of the ideal situation of undamped periodical motion were the planets in their orbits.…