Related papers: The tale of two centres
Pendulums are simple mechanical systems that have been studied for centuries and exhibit many aspects of modern dynamical systems theory. In particular, the double pendulum is a prototypical chaotic system that is frequently used to…
The dynamics of an ensemble of bistable elements with global time-delayed coupling under the influence of noise is studied analytically and numerically. Depending on the noise level the system undergoes ordering transitions and demonstrates…
Our previous study of a system of bodies assumed to move along almost circular orbits around a central mass, approximately described by Hill's equations, is extended to "exotic" [alias non-commutative] particles. For a certain critical…
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…
We consider classical two-dimensional Kepler system with spin-orbit coupling and show that at a sufficiently strong coupling it demonstrates a chaotic behavior. The chaos emerges since the spin-orbit coupling reduces the number of the…
The dynamical symmetry breaking in a two-field model is studied by numerically solving the coupled effective field equations. These are dissipative equations of motion that can exhibit strong chaotic dynamics. By choosing very general model…
Spatial diffusion of particles in periodic potential models has provided a good framework for studying the role of chaos in global properties of classical systems. Here a bidimensional "soft" billiard, classically modeled from an optical…
Einstein-like Lagrangian field theory is developed to describe elastic solid containing dislocations with finite-sized core. The framework of the Riemann-Cartan geometry in three dimensions is used, and the core self-energy is expressed by…
Using two new well defined 4-dimensional potential vectors, we formulate the classical Maxwell's field theory in a form which has manifest Lorentz covariance and SO(2) duality symmetry in the presence of magnetic sources. We set up a…
The topological structures that arise from two-dimensional models are relevant physically and the first step towards understanding more complex systems. In this work, one studies the kink-like solutions of the matter field that emerge in a…
Within the metric structure endowed with two orthogonal space-like Killing vectors a class of solutions of the Einstein-Maxwell-Dilaton field equations is presented. Two explicitly given sub-classes of solutions bear an interpretation as…
Expressions for variables of the center of mass and relative motions for two-body system with different and equal masses in three-dimensional spaces of constant curvature are introduced in the terms of biquaternions. The problem of the…
This paper devoted to proof the existence of stable quasi-periodic motions of the magnetic dipole that is under the action of the external magnetic field and homogeneous field of gravity. For proof this we used the group-theoretic methods…
The aim of this work is to provide a possible philosophical motivation to the variational principles of physics in general and a possible way to unify the axiomatizations of mechanics theories. The leitmotif of this work is a dialectical…
Trajectories in the space of the unitarily inequivalent representations of the canonical commutation relations are shown to be classical trajectories. Under convenient conditions, they may exhibit properties typical of chaotic behavior in…
The problem of motion for different test particles, charged and spinning objects of constant spinning tensor in different versions of bimetric theory of gravity is obtained by deriving their corresponding path and path deviation equations,…
In this paper, we study the dual Anomaly flow, which is a dual version of the Anomaly flow under T-duality. A family of monotone functionals is introduced and used to estimate the dilaton function along the flow. Many examples and…
Group-theoretical approach is applied to study behavior of lossless two-level atoms in a standing-wave laser field. Due to the recoil effect, the internal and external atomic degrees of freedom become coupled. The internal dynamics is…
We define bi-monotone independence, prove a bi-monotone central limit theorem and use it to study the distribution of bi-monotone Brownian motion, which is defined as the two-dimensional operator process with monotone and antimonotone…
It is shown that the groups of Euclidian rotations, rigid motions, proper, orthochronous Lorentz transformations, and the complex rigid motions can be represented by the groups of unit-norm elements in the algebras of real, dual, complex,…