Related papers: A new Visual approach to pendulum period determina…
In 1651 Giovanni Riccioli reported the earliest accurate measurements the acceleration due to gravity, g, from pendulum-timed free fall experiments. The use of Huygens' pendulum formula (published 1673) allows one to deduce the pendulum…
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…
Planar curves with periodically varying curvature arise in the natural sciences as the result of a wide variety of periodic processes. The total curvature of a periodic arc in such curves constrains their symmetry. It is shown how the total…
Time-delayed control in a balancing problem may be a nonsmooth function for a variety of reasons. In this paper we study a simple model of the control of an inverted pendulum by either a connected movable cart or an applied torque for which…
We give practical numerical methods to compute the period matrix of a plane algebraic curve (not necessarily smooth). We show how automorphisms and isomorphisms of such curves, as well as the decomposition of their Jacobians up to isogeny,…
Motivated by recent studies of bifurcations in liquid crystals cells [1,2] we consider a nonlinear pendulum ordinary differential equation in the bounded interval $(-L, L)$ with non-homogeneous mixed boundary conditions (Dirichlet an one…
In a previous paper, we had shown that because of varying angles of incidence there is a varying degree of convolution down a trace and across a gather, necessitating deconvolution operators varying with time and offset. This idea is…
Using the geodesic method and the perturbative approach, we study the deflection of light by time-periodic spherically symmetric gravitational fields. Assuming the weakness of the gravitational field, we derive general formulas that…
Pendulums are simple mechanical systems that have been studied for centuries and exhibit many aspects of modern dynamical systems theory. In particular, the double pendulum is a prototypical chaotic system that is frequently used to…
This study focuses on evaluating three methods used to determine the theoretical gravity in the city of Cusco and their importance in distance education. The first method is based on Newton's law of universal gravitation, obtaining a…
A description of the canonical formulation of lineal gravity minimally coupled to N point particles in a circular topology is given. The Hamiltonian is found to be equal to the time-rate of change of the extrinsic curvature multiplied by…
This study shows that typical pendulum dynamics is far from the simple equation of motion presented in textbooks. A reasonably complete damping model must use nonlinear terms in addition to the common linear viscous expression. In some…
Consider a sequence of independent random isometries of Euclidean space with a previously fixed probability law. Apply these isometries successively to the origin and consider the sequence of random points that we obtain this way. We prove…
Solving for the minimum time bounded acceleration trajectory with prescribed position and velocity at endpoints is a highly nonlinear problem. The methods and bounds developed in this paper distinguish when there is a continuous…
While iterating the quadratic polynomial f_{c}(x)=x^{2}+c the degree of the iterates grows very rapidly, and therefore solving the equations corresponding to periodic orbits becomes very difficult even for periodic orbits with a low period.…
In this paper we give the Bohr-Sommerfeld-Heisenberg quantization of the mathematical pendulum.
Since Galileo's time, the pendulum has evolved into one of the most exciting physical objects in mathematical modeling due to its vast range of applications for studying various oscillatory dynamics, including bifurcations and chaos, under…
We present measurements of the mean energy for an atom optics kicked rotor ensemble close to quantum resonance. Oscillations in the mean energy in this regime are are shown to be in agreement with a quasi--classical pendulum approximation.…
The paths on the {\bf R$^3$} real Euclidean manifold are defined as 2-dimensional simplicial strips; points are replaced by 2-simplexes and the orbits of the action of a one discrete-parameter group on the base manifold becomes a convex…
In this paper we present a straightforward systematic method for the exact and approximate calculation of integrals that appear in formulas for the period of anharmonic oscillators and other problems of interest in classical mechanics.