Related papers: A new Visual approach to pendulum period determina…
One source of beauty in mathematics is totally unexpected connections between two fundamentally different objects. For instance, is it not surprising that the time period of a real simple pendulum is linked with a function arising out of…
Here we study a class of second-order nonautonomous differential equations, and the corresponding planar and spatial systems, from the point of view of fractal geometry. The fractal oscillatority of solutions at infinity is measured by…
A driven pendulum with vertical oscillations of pendulum support (Kapitza pendulum) possesses a number of unusual properties and is a popular object of both analytical and numerical studies. Although some spectacular results can be…
We investigated the common difficulties that students have with concepts related to rotational and rolling motion covered in the introductory physics courses. We compared the performance of calculus- and algebra-based introductory physics…
Vectorial analysis relating to derivation of deflection of light is presented. Curvilinear acceleration is distinguished from the Newtonian polar conic acceleration. The difference between the two is due to the curvature term. Lorentz…
Using concepts of geometric orthogonality and linear independence, we logically deduce the form of the Pauli spin matrices and the relationships between the three spatially orthogonal basis sets of the spin-1/2 system. Rather than a…
The characteristics of drive-free oscillations of a damped simple pendulum under sinusoidal potential force field differ from those of the damped harmonic oscillations. The frequency of oscillation of a large amplitude simple pendulum…
A pendulum powered by high voltage electricity is described. The pendulum consists of two conducting plates(thin foil) separated by copper rods and are insulated from each other. High voltage is applied to these plates through the…
We establish an instructive experiment to investigate the minimum time curve traveled by a small billiard ball rolling in a grooved track under gravity. Our intention is to popularize the concept of \textit{minimum time curve} anew, and to…
Iteration of the quadratic map produces sequences of polynomials whose degrees {\sl explode} as the orbital period grows more and more. The polynomial mixing all 335 period-12 orbits has degree $4020$, while for the $52,377$ period-20…
In this article, the continuous time random walk on the circle is studied. We derive the corresponding generalized master equation and discuss the effects of topology, especially important when Levy flights are allowed. Then, we work out…
We propose a variational symplectic numerical method for the time integration of dynamical systems issued from the least action principle. We assume a quadratic internal interpolation of the state between two time steps and we approximate…
A simple procedure is developed to determine orbital elements of an object orbiting in a central force field which contribute more than three independent celestial positions. By manipulation of formal three point Gauss method of orbit…
We present the Euler--Langrage equations for a many-body system of coupled planar pendulums. Hence, imposing initial condition data, the equations of motion are linearized and later developed in an idealized model for the pseudo-periodicity…
The simplest (3+1)D Regge calculus model (with three-dimensional discrete space and continuous time) is considered which describes evolution of the simplest closed two-tetrahedron piecewise flat manifold in the continuous time. The measure…
We present new periodograms that are effective in distinguishing Doppler shift from spectral shape variability in astronomical spectra. These periodograms, building upon the concept of partial distance correlation, separate the periodic…
I describe how to obtain a rather good experimental determination of the eccentricity of the Earth orbit, as well as the obliquity of the Earth rotation axis, by measuring, over the course of a year, the elevation of the Sun as a function…
The turbulent Prandtl number has been calculated in the two-loop approximation of the $\eps$ expansion of the stochastic theory of turbulence. The strikingly small value obtained for the two-loop correction explains the good agreement of…
The traditional method of finding the average value of a physical quantity often gives wrong results. Another formula of averaging is derived which gives correct results. It is applied to calculation of the average radius of tapering tube…
Uncovering meaningful regularities in complex oscillatory signals is a challenging problem with applications across a wide range of disciplines. Here we present a novel approach, based on the Hilbert transform (HT). We show that temporal…