经典物理
We demonstrate the existence of a complex Hilbert Space with Hermitian operators for calculations in \textit{classical} electromagnetism that parallels the Hilbert Space of quantum mechanics. The axioms of this classical theory are the…
In this article the pursuit problem of objects that moves with different accelerations and initial speeds is studied. Initially, the situation in which the escaping object moves in a straight line is considered. Under this condition, and if…
Set up a charged rectangular-plate capacitor in a uniform $\mathbf{B}$-field. Quasi-statically turn off the $\mathbf{B}$-field - what happens? We show that this seemingly simple induction problem (which appears in a famous undergraduate…
We show that during normal modes of an oscillatory system consisting of a hoop and a cylinder joining their centers by an ideal spring, its central mass does not remain at rest. This effect is due to the resultant external static friction…
Traveling fronts ubiquitous in physics, chemistry, and biology are prone to transverse cellular deformations due to diffusive or convective instabilities. Here we show both theoretically and experimentally that new patterns can be obtained…
Geometric phases provide a unified framework for understanding diverse phenomena in quantum and classical physics. The Pancharatnam-Berry (PB) geometric phase, arising from variation of optical transverse polarization, has transformed light…
Lima and Monteiro [1] derived the buoyant force in a nonuniform gravitational field by applying a gradient version of the divergence theorem to the surface integral of the pressure forces [2]. Here it is outlined an alternate approach in…
In the Comment the procedure for obtaining a solution for the electromagnetic potential, presented in the cited work arxiv:2507.02104, is analyzed. It is shown that the solution obtained by the authors is based on some mathematically…
A point charge between the plates of a capacitor generates an influence charge distribution on the plates that modify the electric field acting upon the point charge. This effect is described by the well-known Dirichlet Green's function for…
Wave manipulation is essential in various applications, including seismic wave protection, sound isolation, and acoustic device design. This study examines the scattering and trapping of antiplane SH waves in a microstructured solid…
We present a novel extension of Hamiltonian mechanics to nonconservative systems built upon the Schwinger-Keldysh-Galley double-variable action principle. Departing from Galley's initial-value action, we clarify important subtleties…
We formulate an optimization of a bicycle ascent time under the constraints of the average, maximum, and minimum powers. In contrast to the first part of this study, we do not restrict the departure to flying starts with an initial speed…
We aim to show that the dimensionless unit angular frequency of a certain mechanical oscillator is realized by a condition involving the Hardy-Ramanujan number 1729. This type of coupled oscillator can be called a Ramanujan's oscillator.
We numerically investigate the stability and linear oscillatory behavior of a naturally diverging mass whose potential energy is harmonically modulated. It is known that in the Kapitza limit, i.e. when the period of modulation is much…
We study mathematical models of binary direct collinear collisions of convex viscoplastic bodies based on two incremental collision laws that employ the Bouc-Wen differential model of hysteresis to represent the elastoplastic behavior of…
In Bell's spaceship paradox, a thread connects two spaceships moving with identical accelerations. As the ships accelerate in lockstep, the tension in the string increases due to the relativistic contraction and the string eventually…
Two-dimensional (planar) rigid-body impact mechanics for application in automobile collisions have been described by a number of researchers over the last several decades. Little has been discussed, however, regarding three-dimensional…
This article proposes an in-depth investigation into the emergence of thermoacoustic waves from a variational formalism rooted in non-equilibrium thermodynamics. Differing from traditional approaches based on linear simplifications, this…
Basic principles of mathematical modeling are reviewed in this book, with the focus on physics and its practical applications, and examples of selected mathematical methods are presented. Most of the models have been imported from physics…
Dynamical magnetic levitation has attracted broad interest in the realm of physics and engineering. The stability analysis of such system is of great significance for practical applications. In this work, we investigate the stable magnetic…