Related papers: Simple Linearizations of the Simple Pendulum for A…
A treatment is given of the precession of a Foucault pendulum by means of two successive rotational transformations of coordinate system. The simplicity and accuracy of this approach is emphasized.
The simplest way to obtain continuous interpolation between two points in high dimensional space is to draw a line between them. While previous works focused on the general connectivity between model parameters, we explored linear…
It is shown that a transparent birefringent element whose eigenstates are a pair of elliptical polarizations with principalaxes along the x and y axes, sandwiched between a pair of orthogonal halfwave plates with principal axes along…
We investigate the nonlinear effect of a pendulum with the upper end fixed to an elastic rod which is only allowed to vibrate horizontally. The pendulum will start rotating and trace a delicate stationary pattern when released without…
In this paper we present a study of the non-linear effects of anharmonicity of the potential of the simple pendulum. In a theoretical reminder we highlight that anharmonicity of the potential generates additional harmonics and the…
This work provides a complete characterization of the solutions of a linear interpolation problem for vector polynomials. The interpolation problem consists in finding n scalar polynomials such that an equation involving a linear…
The formal properties of the recently derived set of linearly independent invariant amplitudes for the electromagnetic production of a pseudoscalar particle from a spin-one particle have been further exploited. The crossing properties are…
We compute the simplest one-loop planar amplitudes in Higgsed ABJM theory at a generic point of the moduli space. We explicitly check that they can be expressed in terms of integrals which are invariant under dual conformal symmetry…
According to Lidstone interpolation theory, an entire function of exponential type $<\pi$ is determined by it derivatives of even order at $0$ and $1$. This theory can be generalized to several variables. Here we survey the theory for a…
Multiple pendulums are investigated numerically and analytically to clarify the nonuniformity of average kinetic energies of particles. The nonuniformity is attributed to the system having constraints and it is consistent with the…
We discuss formulation of Wilson polygon - MHV amplitude duality at the perturbative level in various regularizations. For four gluons it is shown that at one loop one can formulate diagrammatic correspondence interpolating between the…
The analytical solution of the three--dimensional linear pendulum in a rotating frame of reference is obtained, including Coriolis and centrifugal accelerations, and expressed in terms of initial conditions. This result offers the…
Two computational models to be used as tools for experimental research on the retinal implant are presented. In the first model, the electric field produced by a multi-electrode array in a uniform retina is calculated. In the second model,…
We present an analytical description of the large-amplitude stationary oscillations of the finite discrete system of harmonically-coupled pendulums without any restrictions to their amplitudes (excluding a vicinity of $\pi$). Although this…
A compound pendulum of simple geometry was built from a lightweight rod to which a pair of masses are clamped, one above and the other below the axis of rotation. By making the position of the upper mass variable, it was found that the…
A systematic construction of higher order splines using two hierarchies of polynomials is presented. Explicit instructions on how to implement one of these hierarchies are given. The results are limited to interpolations on regular,…
We give a description, in analytic and geometric terms, of the interpolation sequences for the algebra of entire functions of exponential type which are bounded on the real line.
Linearization of coupled second order nonlinear ordinary differential equations (SNODEs) is one of the open and challenging problems in the theory of differential equations. In this paper we describe a simple and straightforward method to…
A generalized gauge fixing which interpolates among the Landau, Coulomb and maximal Abelian gauges is constructed.
The Fourier-based analysis customarily employed to analyze the dynamics of a simple pendulum is here revisited to propose an elementary iterative scheme aimed at generating a sequence of analytical approximants of the exact law of motion.…