Related papers: Quadratic choreographies
We study in this paper the continuous and discrete Euler-Lagrange equations arising from a quadratic lagrangian. Those equations may be thought as numerical schemes and may be solved through a matrix based framework. When the lagrangian is…
We develop in this paper a new framework for discrete calculus of variations when the actions have densities involving an arbitrary discretization operator. We deduce the discrete Euler-Lagrange equations for piecewise continuous critical…
The quantum dynamical systems of identical particles admitting an additional integral quadratic in momenta are considered. It is found that an appropriate ordering procedure exists which allows to convert the classical integrals into their…
Equations of a rotating body with one point constrained to move freely on a plane (dancing top) are deduced from the Lagrangian variational problem. They formally look like the Euler-Poisson equations of a heavy body with fixed point,…
We calculate the quantum corrections to the classical action of a particle with coordinate-dependent mass. The result is made self-consistent by a variational approach, thus making it applicable to strong-couplings and singular potentials.…
We consider the equations of motion of $n$ vortices of equal circulation in the plane, in a disk and on a sphere. The vortices form a polygonal equilibrium in a rotating frame of reference. We use numerical continuation in a boundary value…
In this study we combine the classical models of the massive and massless spinning particles, derive the current-current interaction Lagrangian of the particles from the gauge transformations of the classical spinors, and discuss radiative…
We present a variational approach to obtain periodic solutions of the $N$-body problem, in particular the 'figure-eight' solution for three equal masses. The central idea is to explicitly optimize the \emph{spatial scale} within the…
A new model to study the dynamics of relativistic quantum plasmas using the quantum electrodynamical (QED) approach has been constructed to analyze the quantum effects, relativistic corrections, and electromagnetic interactions. Considering…
We report on figure-eight choreographic solutions to a system of three identical particles interacting through a potential of Lennard-Jones type, $1/r^{12}-1/r^6$ where $r$ is a distance between the particles. By numerical search, we found…
Electromagnetic properties of quark-like particles are examined in a classical field model involving extended dual electromagnetic fields. These can have fractional charges and a confining potential that derives essentially completely from…
The framework of entropic dynamics (ED) allows one to derive quantum mechanics as an application of entropic inference. In this work we derive the classical limit of quantum mechanics in the context of ED. Our goal is to find conditions so…
We study the classical dynamics of a particle in nonrelativistic Snyder-de Sitter space. We show that for spherically symmetric systems, parametrizing the solutions in terms of an auxiliary time variable, which is a function only of the…
We consider classical N-particle system with arbitrary central pair potential. Mechanical equilibrium condition in spherically-symmetric case leads to a nonlinear integro-differential equation for concentration n(r). For special state…
We derive new solutions of the Schr\"odinger equation which describe the motion of particles in the Penning trap. These solutions are direct counterparts of classical orbits. They are obtained by injection of classical trajectories into the…
We have investigated the dynamics of particles in the vicinity of a static spherically symmetric black hole in f(R) gravity. Using the Euler-Lagrange method the dynamical equations of a neutral particle are obtained. Assuming that the…
We present a novel numerical method to calculate periodic orbits for dynamical systems by an iterative process which is based directly on the action integral in classical mechanics. New solutions are obtained for the planar motion of three…
It is demonstrated how all the mechanical equations of classical electrodynamics (CEM) may be derived from only Coulomb's inverse square force law, special relativity and Hamilton's Principle. The instantaneous nature of the Coulomb force…
We study some combinatorial and algebraic properties of certain quadratic algebras related with dynamical classical and classical Yang-Baxter equations. One can find more details about the content of present paper in Extended Abstract.
The Dirac method is used to analyze the classical and quantum dynamics of a particle constrained on a circle. The method of Lagrange multipliers is scrutinized, in particular in relation to the quantization procedure. Ordering problems are…