Classical Physics
A detailed program is proposed in the Lagrangian formalism to investigate the dynamical behavior of a theory with singular Lagrangian. This program goes on, at different levels, parallel to the Hamiltonian analysis. In particular, we…
An asymptotic analysis of the energy functional of a fiber-reinforced composite beam with a periodic microstructure in its cross section is performed. From this analysis the asymptotically exact energy as well as the 1-D beam theory of…
Acoustic analogue computation and signal processing are of great significance, however, it's challenging to realize the acoustic computing devices because of their limitations of single function and complex structure. In this paper, an…
We reexamine a very classical problem, the spinning behavior of the tippe top on a horizontal table. The analysis is made for an eccentric sphere version of the tippe top, assuming a modified Coulomb law for the sliding friction, which is a…
We examine the spinning behavior of egg-shaped axisymmetric bodies whose cross sections are described by several oval curves similar to real eggs with thin and fat ends. We use the gyroscopic balance condition of Moffatt and Shimomura and…
For certain shapes of inclusions embedded in a body, the field inside the inclusion is uniform for some boundary condition. We provide a construction scheme for inclusions of general shapes having such a uniformity property in two…
The Maxwell-Lorentz theory of electrodynamics cannot readily be applied to a system of point charges: the electromagnetic field is not well-defined at the position of a point charge, an energy conservation argument is not obvious, an…
The electrostatics problem of a point charge next to a conducting plane is best solved by placing an image charge placed on the opposite side. For a charge between two parallel planes this can be solved with image charges outside the planes…
We review the scattering from non-linear interfaces containing buckling elastic beams. An illustrative example is discussed here of scattering of linear elastic pressure waves from a two-mass system connected by a non-linear structured…
In all structural models, the section or fiber response is a relation between the strain measures and the stress resultants. This relation can only be expressed in a simple analytical form when the material response is linear elastic. For…
The cavitation of solid elastic spheres is a classical problem of continuum mechanics. Here, we study this problem within the context of "stochastic elasticity" where the constitutive parameters are characterised by probability density…
Two triangular factorizations of the deformation gradient tensor are studied. The first, termed the Lagrangian formulation, consists of an upper-triangular stretch premultiplied by a rotation tensor. The second, termed the Eulerian…
We present a new method for computing orbits in the perturbed two-body problem: the position and velocity vectors of the propagated object in Cartesian coordinates are replaced by eight orbital elements, i.e., constants of the unperturbed…
Invariance in duality transformation, the self-dual property, has important applications in electromagnetic engineering. In the present paper, the problem of most general linear and local boundary conditions with self-dual property is…
In 1687 Isaac Newton published PHILOSOPHI\AE \ NATURALIS PRINCIPIA MATHEMATICA, where the classical analytic dynamics was formulated. But Newton also formulated a discrete dynamics, which is the central difference algorithm, known as the…
A recent Letter has reported that sound waves can carry gravitational mass. I analyze this effect in a Hooke's law solid, considering a wave packet moving in the $z$ direction with an amplitude that is independent of $x$ and $y$. The…
In this paper we present a new extended complex nonlinear Klein-Gordon Lagrangian density, which bears a single non-topological soliton solution with a specific rest frequency $\omega_{s}$ in $1+1$ dimensions. There is a proper term in the…
A short historical account of the curves related to the two-dimensional floating bodies of equilibrium and the bicycle problem is given. Bor, Levi, Perline and Tabachnikov found, quite a number had already been described as Elastica by…
The domestic windows in the exterior building facade play a significant role in sound insulation against outdoor airborne noise. The prediction of their acoustic performances is classically carried out in laboratory according to standard…
Poynting theorem plays a very important role in analyzing electromagnetic phenomena. The electromagnetic power flux density is usually expressed with the Poynting vector. However, since Poynting theorem basically focuses on the power…