Related papers: Classical dynamics on triangleland
Relativistic dynamics of a charged particle in time-dependent electromagnetic fields has theoretical significance and a wide range of applications. It is often multi-scale and requires accurate long-term numerical simulations using…
In this paper, we study the geodesic motion in spherically symmetric electro-vacuum Euclidean solutions of the Einstein equation. There are two kinds of such solutions: the Euclidean Reissner-Nordstr\"{o}m (ERN) metrics, and the…
The variational principle and the corresponding differential equation for geodesic circles in two dimensional (pseudo)-Riemannian space are being discovered. The relationship with the physical notion of uniformly accelerated relativistic…
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…
Particles traveling in aligned crystals at small angles w.r.t. crystallographic axes or planes are principally steered by the continuous Lindhard potential. This interaction conserves the energy E, the longitudinal momentum p_parallel, the…
This work may be defined as a modern philosophical approach to theoretical physics. Since ancient times science and philosophy evolved in parallel, thus renewing from time to time the epochal paradigms of human thought. We could not…
With toy modelling of conceptual aspects of quantum cosmology and the problem of time in quantum gravity in mind, I study the classical and quantum dynamics of the pure-shape (i.e. scale-free) triangle formed by 3 particles in 2-d. I do so…
We investigate deviations from the plane wave model in the interaction of charged particles with strong electromagnetic fields. A general result is that integrability of the dynamics is lost when going from lightlike to timelike or…
We investigate the relativistic generalization of the classical St\"{o}rmer problem, which describes the motion of charged particles in a purely magnetic dipole field. By incorporating special relativistic effects, the particle dynamics is…
I investigate qualitatively significant regions of the configuration space for the classical and quantum mechanics of the relational quadrilateral in 2-d. This is relational in the sense that only relative ratios of separations, relative…
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…
The interaction of the electric and magnetic dipole moments of a particle with the electromagnetic field is investigated in an approach that deals with four-dimensional (4D) geometric quantities. The new commutation relations for the 4D…
The effective equations of motion for a point charged particle taking account of radiation reaction are considered in various space-time dimensions. The divergencies steaming from the pointness of the particle are studied and the effective…
There are known problems of Lorentz-Dirac equation for moving with acceleration charged particle in classical electrodynamics. The model of extended in one dimension particle is proposed and shown that electromagnetic self-interaction can…
Classical relativistic system of point particles coupled with an electromagnetic field is considered in the three-dimensional representation. The gauge freedom connected with the chronometrical invariance of the four-dimensional description…
With the aid of a Fermi-Walker chart associated with an orthonormal frame attached to a time-like curve in spacetime, a discussion is given of relativistic balance laws that may be used to construct models of massive particles with spin,…
The Snyder model is an example of noncommutative spacetime admitting a fundamental length scale $\beta$ and invariant under Lorentz transformations, that can be interpreted as a realization of the doubly special relativity axioms. Here, we…
We present a relativistic quantum mechanics of a point mass with absolute thermodynamic time and temperature, combined to a single complex parameter of evolution. In this theory, the geometric time is introduced as one of space-time…
The purpose of this paper is to show that: when a single particle moving under 3-proper time (three-dimensional time), the trajectories of a classical particle are equivalent to a quantum field with spin. Three-proper time models are built…
We lay down the foundations of particle dynamics in mechanical theories that satisfy the relativity principle and whose kinematics can be formulated employing reference frames of the type usually adopted in special relativity. Such…