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We show how several important classical problems, with positive definite potential energy, can be solved by starting from the factorization of the total mechanical energy using complex numbers. In particular, we derive in a new way exact…
A research on a possibility of trapping a particle with permanent electric dipole in an electrostatic field has been conducted. For cylindrical coaxial electrodes, Keplerian orbits for some particles were revealed. The exact criterion of…
We present a simple choice of integration variables that can be used to exploit the near-integrable character of problems in celestial mechanics. The approach is based on the well-known principle of variation of parameters: instead of…
The nature of boundedness of orbits of a particle moving in a central force field is investigated. General conditions for circular orbits and their stability are discussed. In a bounded central field orbit, a particle moves clockwise or…
It is shown how point charges and point dipoles with finite self-energies can be accomodated into classical electrodynamics. The key idea is the introduction of constitutive relations for the electromagnetic vacuum, which actually mirrors…
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…
The paper analyzes a Lagrangian system which is controlled by directly assigning some of the coordinates as functions of time, by means of frictionless constraints. In a natural system of coordinates, the equations of motions contain terms…
When studying (or teaching) classical electromagnetism, one is bound to deal with the electric field of an ideal electric dipole, as well as its magnetic counterpart. A careful analysis then reveals that each of those fields must include,…
Neural networks have provided powerful approaches to solve various scientific problems. Many of them are even difficult for human experts who are good at accessing the physical laws from experimental data. We investigate whether neural…
I discuss the influence of adding the air resistance and the kinetic friction to the classical mechanics homework-problem: finding the motion of a body sliding down a hemispherical hill. For a physically realistic ($\propto v^2$) form of…
A global analysis is presented of solutions for Laplace's equation on three-dimensional Euclidean space in one of the most general orthogonal asymmetric confocal cyclidic coordinate systems which admit solutions through separation of…
The method of images to solve certain electrostatic boundary-value problems is taught worldwide in undergraduate-level physics courses. Though it is also possible to employ this technique for solving magnetostatic boundary value problems,…
We study mechanical systems subject to constraint functions that can be dependent at some points and independent at the rest. Such systems are modelled by means of generalized codistributions. We discuss how the constraint force can…
We study the dynamics of planons, particles whose mobility is restricted to a plane, through the classification of coadjoint orbits and unitary irreducible representations of the centrally extended planon group. Planons are closely related…
Electromagnetic waves arise in many area of physics. Solutions are difficult to find in the general case. In this paper, we numerically integrate Maxwell equations in a 3D spherical polar coordinate system. Straightforward finite difference…
The classical dynamics of a particle that is driven by a rapidly oscillating potential (with frequency $\omega$) is studied. The motion is separated into a slow part and a fast part that oscillates around the slow part. The motion of the…
Consider the dynamics of two point masses on a surface of constant curvature subject to an attractive force analogue of Newton's inverse square law. When the distance between the bodies is sufficiently small, the reduced equations of motion…
We first demonstrate how our general intuition of pseudoforces has to navigate around several pitfalls in rotating frames. And then, we proceed to develop an intuitive understanding of the different components of the pseudoforces in most…
In this series of eight papers we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In this part we consider a model for spin-orbital motion: orbital…
A core level of basic information for physics is identified, based on an analysis of the characteristics of the parameters space, time, mass and charge. At this level, it is found that certain symmetries operate, which can be used to…