经典物理
School and undergraduate students are almost always taught the equations of electromagnetism using a set of conventions that are described as the SI. More advanced students are often introduced to different conventions that produce…
The transformation formulas between two inertial frames for the minimum phase velocity and the phase velocity in an arbitrary direction are given. The derived transformation formula for the reciprocal of the phase velocity along the…
We consider a quite general problem concerning a linear free oscillation of a discrete mass-spring-damper system. This discrete sub-system is embedded into a one-dimensional continuum medium described by the linear telegraph equation. In a…
We present a numerical solution of the nonlinear differential equation for a pendulum with an elastic string on the rotating Earth, for different values of string stiffness at different geographic latitudes.
The study is focused on the dispersion properties of a wire medium formed by a rectangular lattice of parallel wires at the frequencies close to its plasma frequency. While the effective medium theory predicts isotropic behaviour of…
The two-thirds power law is a link between angular speed $\omega$ and curvature $\kappa$ observed in voluntary human movements: $\omega$ is proportional to $\kappa^{2/3}$. Squared jerk is known to be a Lagrangian leading to the latter law.…
We study the classical dynamics of a system comprising a pair of Kerr-Duffing nonlinear oscillators, which are coupled through a nonlinear interaction and subjected to a parametric drive. Using the rotating wave approximation (RWA), we…
The singular parametric oscillators obtained from the one-parameter Darboux deformation/transformation effected upon the classical harmonic oscillator are introduced and discussed in some detail using sin(omega_0 t) and cos(omega_0 t) as…
A wavepacket (electromagnetic or otherwise) within an isotropic and homogeneous space can be quantized on a regular lattice of discrete k-vectors. Each k-vector is associated with a temporal frequency omega; together, k and omega represent…
The Chu circuit model provides the basis for analyzing the minimum radiation quality factor, Q, of a given spherical mode. However, examples of electrically large spherical radiators readily demonstrate that this Q limit has limitations in…
In a full 3D context, we study a projectile subject to linear drag, a non-uniform gravitational field, time-dependent wind, and parameterized atmospheric thinning. In this general context, we provide integral solutions, exact to $\mathcal{…
A new efficient approach for searching three-body periodic equal-mass collisionless orbits passing through Eulerian configuration is presented. The approach is based on a symmetry property of the solutions at the half period. Depending on…
In the recent years constructing time-invariant spatial-focusing beampatterns by using frequency diverse arrays (FDAs) is conveyed in several papers. Further than time-invariant spatial-focusing beampatterns, the unfeasibility of…
It is well known that two permanent magnets of fixed orientation will either always repel or attract one another regardless of the distance between them. However, if one magnet is rotated at sufficient speed, a stable position at a given…
In this study, we investigate and compare formulations for computing shape derivatives in bi-material level-set optimization with precise modeling of the interface. The level-set function is parameterized using B-splines, whose coordinates…
The behavior of the electromagnetic field near a common edge of a resistive half-plane and a perfectly conducting wedge is investigated. The possible appearance besides power terms also of logarithmic functions in the field expansions at…
Kirchhoff's Current Law is an essential tool in the design of circuits that operate very quickly, faster than nanoseconds. But Kirchhoff's current is often identified as the flow of particles. The continuity equation or the Maxwell-Ampere…
The Sommerfeld-Page equation describes the non-relativistic dynamics of a classical electron modeled by a sphere of finite size with a uniform surface charge density. The Sommerfeld-Page equation is a delay differential equation, and almost…
A confined, slow-moving, accelerating electron is shown to emit thermal radiation. Since laboratories face spatial constraints when dealing with rectilinear motion, focusing on a finite total travel distance combines the benefits of simple…
The stress as a response to strain prescribed as a harmonic excitation is examined in both transient and steady state regime for the viscoelastic body modeled by thermodynamically consistent fractional anti-Zener and Zener models by the use…