We solve exactly the classical non-relativistic Landau–Lifshitz equations of motion for a charged particle moving in a Coulomb potential, including radiation damping. The general solution involves the Painlevè transcendent of type II. It confirms our physical intuition that a negatively charged classical particle will spiral into the nucleus, supporting the validity of the Landau–Lifshitz equat...

In this paper we use Jacobi fields to describe the motion of a charged particle in the classical gravitational, electromagnetic, and Yang-Mills fields. ∗ E-mail: [email protected]

We solve for the motion of charged particles in a helical time-periodic ABC (Arnold-Beltrami-Childress) magnetic field. The magnetic field lines of a stationary ABC field with coefficients A=B=C=1 are chaotic, and we show that the motion of a charged particle in such a field is also chaotic at late times with positive Lyapunov exponent. We further show that in time-periodic ABC fields, the kine...

Let us remind that Sommerfeld model of charged rigid sphere [1] (Sommerfeld particle) is the simplest theoretical model to take into consideration the ”back-reaction” of self-electromagnetic field on equation of motion of a radiating extended charged body (for point-like charge we have the known LorentzDirac equation with all its problems: renormalization of mass, preacceleration, runaway solut...

The identity of classical motion is established for two physically different models, one of which is the relativistic particle with torsion, whose action contains higher derivatives and which is the effective system for the statistically charged particle interacting with the Chern-Simons U(1) gauge field, and another is the (2+1)dimensional relativistic charged particle in external constant ele...

In classical mechanics, the motion of a charged particle depends only on the electric and magnetic tension fields E and B; the potentials A0 and A do not have any direct effect. Also, the motion depends only on the E and B fields along the particle’s world-line — the EM fields in some volume of space the particle never goes through do not affect it at all. But in quantum mechanics, interference...