Classical Physics
Precise manipulation of the direction and re-direction of vibrational wave energy is a key demand in wave physics and engineering. We consider the paradigm of a finite frame-like structure and the requirement to channel energy away from…
Bayesian mechanics is a new approach to studying the mathematics and physics of interacting stochastic processes. Here, we provide a worked example of a physical mechanics for classical objects, which derives from a simple application…
An exact invariant is derived for $n$-degree-of-freedom Hamiltonian systems with general time-dependent potentials. The invariant is worked out in two equivalent ways. In the first approach, we define a special {\it Ansatz\/} for the…
I point out and diagnose an error in a figure in a textbook on classical physics. The error helps to illustrate a pitfall encountered when dealing with the shapes of objects, and perhaps also reflects general cultural attitudes in physics.…
We revisit the problem of constructing one-dimensional acoustic black holes. Instead of considering the Euler-Bernoulli beam theory, we use Timoshenko's approach instead, which is known to be more realistic at higher frequencies. Our goal…
The dynamics of some non-conservative and dissipative systems can be derived by calculating the first variation of an action-dependent action, according to the variational principle of Herglotz. This is directly analogous to the variational…
How will the electrostatic interaction between two point charges change if they are shielded from the other by a dielectrical slab? While the physical setting of this electromagnetic problem is relatively simple, it is easy to be wronged…
Analytically, without magnetostatic approximation, the problem of electromagnetic wave propagation along arbitrary direction in a tangentially magnetized bihyrotropic layer has been solved. It is found that one can bring the Maxwell…
The usual radiation self-force of a point charge is obtained in a mathematically exact way and it is pointed out to that this does not call forth that the spacetime motion of a point charge obeys the Lorentz--Abraham--Dirac equation.
This paper is a critical study of non-standard Maxwellian electrodynamics. It explores two important topics: the inclusion of both magnetic and electric charge to produce what it calls Extended Electrodynamics, and the existence of a…
Cartesian harmonic tensors are completely symmetric traceless tensors in three dimensional space constructed from the direct product of unit vectors. They are useful in generating expressions for the angular coupling of spherical harmonics…
Over the past 30 years, Artificial Magnetic Conductors (AMCs) have generated immense interest in the microwave community. However, their description has been restricted to crude RLC design or subsidiary transmission-line network modelling.…
Elastic metamaterials made from locally resonant arrays have been developed as effective ways to create band gaps for elastic or acoustic travelling waves. They work by implementing stationary states in the structure that localise and…
In the recent work [1], authors discussed the relationship between the two of Euler angles assuming that it can be used to describe some effects in the theory of a rigid body. I show that this assumption is not properly justified.
It is evident that the positions of 4 bodies in $d>2$ dimensional space can be identified with vertices of a tetrahedron. Square of volume of the tetrahedron, weighted sum of squared areas of four facets and weighted sum of squared edges…
The swinging counterweight trebuchet was at its full blossom in the Late Middle Ages an artillery piece of great importance that could destroy the defenses of castles under siege by bombardment with stones from considerable distances. The…
Ideal gas is the most fundamental and simple system in thermodynamics, which has extensive applications in energy research and engineering. By reviewing the physical concept of ideal gas, it is found that the current understanding of ideal…
Transverse Kerker effect is known by the directional scattering of an electromagnetic plane wave perpendicular to the propagation direction with nearly suppression of both forward and backward scattering. Compared with plane waves,…
For the undamped Kepler potential the lack of precession has historically been understood in terms of the Runge-Lenz symmetry. For the damped Kepler problem this result may be understood in terms of the generalization of Poisson structure…
A freely falling chain from a cup at certain height can jump. The process can be divided into two parts: a stable suspension and an accelerating procedure. Variational principle and force analysis demonstrate that the shape of stable…