Related papers: Relativistic formulation of curl force, relativist…
In this present communication the integrable modulation problem has been applied to study parametric extension of the Kapitza rotating shaft problem, which is a protypical example of curl force as formulated by Berry and Shukla in [J. Phys.…
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…
A driven pendulum with vertical oscillations of pendulum support (Kapitza pendulum) possesses a number of unusual properties and is a popular object of both analytical and numerical studies. Although some spectacular results can be…
A toroidal trap combined with external time-dependent electric field can be used for implementing different dynamical regimes of matter waves. In particular, we show that dynamical and stochastic acceleration, localization and…
We study particle dynamics under curl forces. These forces are a class of non-conservative, non-dissipative, position-dependent forces that cannot be expressed as gradient of a potential function. We show that the fundamental quantity of…
We consider the quantum simulation of relativistic quantum mechanics, as described by the Dirac equation and classical potentials, in trapped-ion systems. We concentrate on three problems of growing complexity. First, we study the…
The rotating saddle not only is an interesting system that is able to trap a ball near its saddle point, but can also intuitively illustrate the operating principles of quadrupole ion traps in modern physics. Unlike the conventional models…
We present a novel technique to obtain relativistic corrections to the central force problem in the Lagrangian formulation, using a generalized potential energy function. We derive a general expression for a generalized potential energy…
The relativistic transformation properties of the heavy quark-antiquark interaction potential are considered in the framework of the relativistic quark model. A special attention is paid to the long-range (confining) contribution to the…
One of the many surprising results found in the mechanics of rotating systems is the stabilization of a particle in a rapidly rotating planar saddle potential. Besides the counterintuitive stabilization, an unexpected precessional motion is…
The canonical method of constrained system is discussed. The equations of motion for a free relativistic spinning particle are obtained without using gauge fixing conditions. The quantization of this model is discussed.
Using to a minimum extent special relativity input, and relying on the Lorentz-force expression for the force acting on a charged particle in motion under the influence of electric (E) and magnetic (B) fields, the Maxwell curl equations are…
We consider an inverse variational problem for the lines of constant curvature in (pseudo-)Euclidean two-, three-, and four-dimensional spaces. The accumulated results are physically meaningful in the case of relativistic mechanics of…
For the closed relativistic string carrying a pointlike mass the exact solutions of the dynamical equations are obtained and studied. These solutions describe states of the mentioned system moving in Minkowski space and also in the space…
The turbulent jets are usually described by classical velocities. The relativistic case can be treated starting from the conservation of the relativistic momentum. The two key assumptions which allow to obtain a simple expression for the…
It is proved that Special Relativity imposes constraints on the structure of fundamental forces. The orthogonality of the 4-force exerted on an elementary particle and its 4-velocity is discussed. The significance of the energy-momentum…
We extend the theory of Kapitza stabilization within the complex domain, i.e. for the case of an imaginary oscillating potential. At a high oscillation frequency, the quasi-energy spectrum is found to be entirely real-valued, however a…
Recent work has shown the existence of a relativistic effect present in a single component non-equilibrium fluid, corresponding to a heat flux due to an electric field. The treatment in that work was limited to a four-dimensional Minkowksi…
The Relativistic one dimensional Coulomb problem was studied by means of the Path Integral Monte Carlo method. Relativistic and non-relativistic regimes of this problem were investigated. The relativistic regime appears at small masses of…
The classical rotation is not self-consistent in the framework of the special theory of relativity. the Relativistic rotation is obtained, which takes the relativistic effect into account. It is demonstrated that the angular frequency of…