Related papers: Huygens' cycloidal pendulum: an elementary derivat…
The motion of a pendulum is described as Simple Harmonic Motion (SHM) in case the initial displacement given is small. If we relax this condition then we observe the deviation from the SHM. The equation of motion is non-linear and thus…
We present a simple approach to discrete q-Hermite polynomials with special emphasis on analogies with the classical case.
This teaching article describes a simple and low-cost methodology for studying electrical transport and constructing basic sensor devices using everyday stationery items, including pencils, paper, and a handheld multimeter. The approach is…
We discuss a version of the fundamental theorem of calculus in several variables and some applications, of potential interest as a teaching material in undergraduate courses.
The motion of a classical pendulum in a gravitational field of strength g is explored. The complex trajectories as well as the real ones are determined. If g is taken to be imaginary, the Hamiltonian that describes the pendulum becomes…
Proceeding like Newton with a discrete time approach of motion and a geometrical representation of velocity and acceleration, we obtain Kepler's laws without solving differential equations. The difficult part of Newton's work, when it calls…
In this paper we show that there are applications that transform the movement of a pendulum into movements in $\mathbb{R}^3$. This can be done using Euler top system of differential equations. On the constant level surfaces, Euler top…
In this paper, we introduce discrete conics, polygonal analogues of conics. We show that discrete conics satisfy a number of nice properties analogous to those of conics, and arise naturally from several constructions, including the…
An investigation of classical fields with fractional derivatives is presented using the fractional Hamiltonian formulation. The fractional Hamilton's equations are obtained for two classical field examples. The formulation presented and the…
The motion of a simple pendulum in a uniform gravitational field can be described by the solution of a second-order differential equation, nonlinear differential equation. In practice we solve this equation using the small angle…
Simple necessary and sufficient conditions for a $n$-tuple of noncommutative polynomials to be a cyclic gradient are given and similarly for a noncommutative polynomial to have a vanishing cyclic gradient. Connections with free probability…
We propose a simple derivation of an upper bound for the perimeter of an ellipse. The procedure, which relies on the use of elliptic integrals, consists in introducing, via inequalities and convexity properties, specific integrals which can…
Leibniz algebras generated by one element, called cyclic, provide simple and illuminating examples of many basic concepts. It is the purpose of this paper to illustrate this fact.
Projectile motion is a constant theme in introductory-physics courses. It is often used to illustrate the application of differential and integral calculus. While most of the problems used for this purpose, such as maximizing the range, are…
We show how one can construct a differential calculus over an algebra where position variables x and momentum variables p have be defined. As the simplest example we consider the one-dimensional q-deformed Heisenberg algebra. This algebra…
In this note we present a symbolic pseudo-differential calculus on the Heisenberg group. We particularise to this group our general construction [4,3,2] of pseudo-differential calculi on graded groups. The relation between the Weyl…
During the process of teaching the concept of derivative, it is common and natural to refer to geometric interpretations, such as the use of the tangent line and the maximum and minimum points of a function, to illustrate the scope of the…
The mathematical pendulum is traditionally solved using a Jacobi elliptic functions. We solve it here using the Weierstrass elliptic function. Every initial condition of the pendulum produces an elliptic curve and a point which by the…
We outline an unified introduction to the evolution equations of classical and quantum systems intended for a high school students audience. The attempt consists in circumventing the lack of mathematical knowledge with the use of simplified…
The change of the plane of oscillation of a Foucault pendulum is calculated without using equations of motion, the Gauss-Bonnet theorem, parallel transport, or assumptions that are difficult to explain.