Related papers: Chaos and Maps in Relativistic Dynamical Systems
A complete exposition of the rest-frame instant form of dynamics for arbitrary isolated systems (particles, fields, strings, fluids)admitting a Lagrangian description is given. The starting point is the parametrized Minkowski theory…
The Lorentz transformations are represented on the ball of relativistically admissible velocities by Einstein velocity addition and rotations. This representation is by projective maps. The relativistic dynamic equation can be derived by…
It is shown that a nonrelativistic mechanical system involving a general nonrelativistic potential V(|r1-r2|) between point particles at positions r1 and r2 can be extended to a Lagrangian system which is invariant under Lorentz…
We consider a generalization of the classical nonrelativistic St\"{o}rmer problem, describing the motion of charged particles in a purely magnetic dipole field, by taking into account the effects of the dissipation, assumed to be of…
We revisit the nonrelativistic problem of a bound, charged particle subject to the random zero-point radiation field (ZPF), with the purpose of revealing the mechanism that takes it from the initially classical description to the final…
We report the discovery of an exact mapping from Galilean time and space coordinates to Minkowski spacetime coordinates, showing that Lorentz covariance and the spacetime construct are consistent with the existence of a dynamical 3-space,…
The dynamic of a classical system can be expressed by means of Poisson brackets. In this paper we generalize the relation between the usual non covariant Hamiltonian and the Poisson brackets to a covariant Hamiltonian and new brackets in…
The study of chaos in relativistic systems has been hampered by the observer dependence of Lyapunov exponents (LEs) and of conditions, such as orbit boundedness, invoked in the interpretation of LEs as indicators of chaos. Here we establish…
In relativistic mechanics the energy-momentum of a free point mass moving without acceleration forms a four-vector. Einstein's celebrated energy-mass relation E=mc^2 is commonly derived from that fact. By contrast, in Newtonian mechanics…
In this paper we define a causal Lorentz covariant noncommutative (NC) classical Electrodynamics. We obtain an explicit realization of the NC theory by solving perturbatively the Seiberg-Witten map. The action is polynomial in the field…
We study long-range interacting systems perturbed by external stochastic forces. Unlike the case of short-range systems, where stochastic forces usually act locally on each particle, here we consider perturbations by external stochastic…
Starting from a covariant cycle-averaged Lagrangian the relativistic oscillation center equation of motion of a point charge is deduced and analytical formulae for the ponderomotive force in a travelling wave of arbitrary strength are…
The Lorentz force equations provide a partial description of the geodesic motion of a charged particle on a four-manifold. Under the hypothesis that Maxwell's equations express symmetry properties of the Ricci tensor, the full…
Other than scattering problems where perturbation theory is applicable, there are basically two ways to solve problems in physics. One is to reduce the problem to harmonic oscillators, and the other is to formulate the problem in terms of…
We make a critical comparison of relativistic and non-relativistic classical and quantum mechanics of particles in inertial frames and of the open problems in particle localization at the two levels. The solution of the problems of the…
The classical and the quantal problem of a particle interacting in one-dimension with an external time-dependent quadratic potential and a constant inverse square potential is studied from the Lie-algebraic point of view. The integrability…
Despite the periodic kicks, a linear kicked rotor (LKR) is an integrable and exactly solvable model in which the kinetic energy term is linear in momentum. It was recently shown that spatially interacting LKRs are also integrable, and…
Random magnetic field configurations are ubiquitous in nature. Such fields lead to a variety of dynamical phenomena, including localization and glassy physics in some condensed matter systems and novel transport processes in astrophysical…
The behaviour of an electron in a potential that resembles that of a bidimensional solid with a perpendicular magnetic field applied is studied from a classical point of view. This problem presents the standard features of chaos and some…
A consistent classical and quantum relativistic mechanics can be constructed if Einstein's covariant time is considered as a dynamical variable. The evolution of a system is then parametrized by a universal invariant identified with…