Related papers: The Falling Time of an Inverted Plane Pendulum
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…
The exponential trapezoidal rule is proposed and analyzed for the numerical integration of semilinear integro-differential equations. Although the method is implicit, the numerical solution is easily obtained by standard fixed-point…
In their activity, the traders approximate the rate of return by integer multiples of a minimal one. Therefore, it can be regarded as a quantized variable. On the other hand, there is the impossibility of observing the rate of return and…
Fractional calculus represents a natural tool for describing relativistic phenomena in pseudo-Euclidean space-time. In this study, Fractional modified special relativity is presented. We obtain fractional generalized relation for the time…
The Bertrand's theorem can be formulated as the solution of an inverse problem for a classical unidimensional motion. We show that the solutions of these problems, if restricted to a given class, can be obtained by solving a numerical…
We extend the mathematical model based on stochastic differential equations describing the error gained by an atomic clock to the cases of anomalous behavior including jumps and an increase of instability. We prove an exact iterative…
The dynamics of a hollow cylinder containing granules and rolling down an inclined plane was investigated. A theoretical approach for investigating the behaviour of such a cylinder was proposed. The critical angle of the plane that allows…
This paper deals with the inverse problem of recovering an arbitrary number of fractional damping terms in a wave equation. We develop several approaches on uniqueness and reconstruction, some of them relying on Tauberian theorems on the…
The fermionic relative entropy in two-dimensional Rindler spacetime is studied using both modular theory and the reduced one-particle density operators. The methods and results are compared. A formula for the relative entropy for general…
Evolution of a particle in an inverse square potential is studied. We derive an equation of motion for $\left<r^2\right>$ and solve it exactly. It gives us a possibility to identify the conditions under which a falling of a quantum particle…
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.…
Time-integration for lumped parameter systems obeying implicit Bingham-Kelvin constitutive models is studied. The governing system of equations describing the lumped parameter system is a non-linear differential-algebraic equation and needs…
The tunneling time is here investigated by means of an electromagnetic model, for a system where a gap, between two parallel planes, acts as a classically-forbidden region for an impinging pulse with incidence angle larger than the critical…
The Lorentz integral transform method is briefly reviewed. The issue of the inversion of the transform, and in particular its ill-posedness, is addressed. It is pointed out that the mathematical term ill-posed is misleading and merely due…
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…
Quantum transition amplitudes are formulated for a model system with local internal time, using path integrals. The amplitudes are shown to be more regular near a turning point of internal time than could be expected based on existing…
The solid angle subtended by a right circular cylinder at a point source located at an arbitrary position generally consists of a sum of two terms: that defined by the cylindrical surface ($\Omega_{cyl}$) and the other by either of the end…
This paper aims to show how to guide students with a familiar example to extract as much physics as possible before jumping into mathematical calculation. The period for a physical pendulum made up of a uniform rod is changed by attaching a…
In this article we give an algorithm for computing the integral closure of a reduced Noetherian ring R, in case this integral closure is finitely generated over R.
This article proposes a mathematical model of an inverted analemmatic sundial, provides formulas for calculating the coordinates of their hour markers. On the example of the Belogorsk sundial, a method is described for determining the…