经典物理
The paper is concerned with the problem of toppling propagation velocity in elastic, domino-like mechanical systems. We build on the work of Efthimiou and Johnson, who developed the theory of perfectly elastic collisions of thin rigid…
This article develops the design of a sound synthesis model of a woodwind instrument by modal decomposition of the input impedance, taking into account viscothermal losses as well as localized nonlinear losses at the end of the resonator.…
We consider the modified Emden equation (MEE) and introduce its most general solution, using the most general solution for the simple harmonic oscillator's linear dynamical equation (i.e., the initial conditions shall be identified by the…
In statistical mechanics, the generally called Stirling approximation is actually an approximation of Stirling's formula. In this article, it is shown that the term that is dropped is in fact the one that takes fluctuations into account.…
We analyze the physics of a type of homopolar motor comprising an AA battery with two cylindrical neodymium magnets on each end that roll inside a metal cylindrical tube. The motion of the motor results from the interaction between the…
A relativistically invariant expression for the magnetic and electric helicities of free electromagnetic field through the currents, which created those field, are derived. It is demonstrated that for radiative fields (e.g. laser pulses)…
The term `sub-wavelength' is commonly used to describe innovative sound-absorbing structures usually labeled as `metamaterials'. Such structures, however, inherently do not bring groundbreaking advancements. This study addresses the…
We investigate the ground state properties of rectangular dipole lattices on curved surfaces. The curved geometry can `distort' the lattice and lead to dipole equilibrium configurations that strongly depend on the local geometry of the…
Porous acoustic absorbers have excellent properties in the low-frequency range when positioned in room edges, therefore they are a common method for reducing low-frequency reverberation. However, standard room acoustic simulation methods…
An elastic rod, straight in its undeformed state, has a mass attached at one end and a variable length, due to a constraint at the other end by a frictionless sliding sleeve. The constraint is arranged with the sliding direction parallel to…
The dispersion curves of (elastic) waveguides frequently exhibit crossings and osculations (also known as veering, repulsion, or avoided crossing). Osculations are regions in the dispersion diagram where curves approach each other…
A simple and clear method is proposed to calculate the averaged motion of the apsis line in the Moon orbit. The obtained result is $3^{\circ}1'12''$ for the starry period of the Moon revolution around the Earth or $40^{\circ}22'48''$ per…
Fisher information is a lower bound on the uncertainty in the statistical estimation of classical and quantum mechanical parameters. While some deterministic dynamical systems are not subject to random fluctuations, they do still have a…
Numerical transfer matrices have been widely used in the study of wave propagation and scattering. These may be viewed as descretizations of a recently introduced fundamental notion of transfer matrix which admits a representation in terms…
Maxwell's fisheye is a paradigm for an absolute optical instrument with a refractive index deduced from the stereographic projection of a sphere on a plane. We investigate experimentally the dynamics of flexural waves in a thin plate with a…
Derivation of the Lorentz transformation without the use of Einstein's Second Postulate is provided along the lines of Ignatowsky, Terletskii, and others. This is a write-up of the lecture first delivered in PHYS 4202 E&M class during the…
Equations of motion are derived for (visco)elastic, self-gravitating, and variably-rotating planets. The equations are written using a decomposition of the elastic motion that separates the body's elastic deformation from its net…
We consider the impact of a ring crack within a rotating hollow cylinder of fixed height under axisymmetric (torsion) loading. The form of the displacement is obtained from the equation of motion using the Fourier sin transform. The…
The question of the title is a famous puzzle in the field of recreational mathematics, and can be addressed by several approaches. A compilation of solutions, some of them very ingenious, can be found in [1]. In this contribution we present…
We formulate a phenomenological model to study the power applied by a cyclist on a velodrome\, -- \,for individual timetrials\, -- \,taking into account the straights, circular arcs, connecting transition curves and banking. The dissipative…