Related papers: On the Equilibria and Bifurcations of a Rotating D…
Using continuation methods, we study the global solution structure of periodic solutions for a class of periodically forced equations, generalizing the case of relativistic pendulum. We obtain results on the existence and multiplicity of…
We study a three-dimensional dynamical system in two slow variables and one fast variable. We analyze the tangency of the unstable manifold of an equilibrium point with "the" repelling slow manifold, in the presence of a stable periodic…
A classical double oscillator model, that includes in certain parameter limits, the standard harmonic oscillator and the inverse oscillator, is interpreted as a dynamical system. We study its essential features and make a qualitative…
The looping pendulum is a simple physical system consisting of two masses connected by a string that passes over a rod. We derive equations of motion for the looping pendulum using Newtonian mechanics, and show that these equations can be…
We present an experimental study of the Duffing--Holmes oscillator with a double-well potential, implemented as an analog electronic circuit under periodic external forcing. By systematically varying the forcing amplitude and frequency, we…
This work deals with planar dynamical systems with and without noise. In the first part, we seek to gain a refined understanding of such systems by studying their differential-geometric transformation properties under an arbitrary smooth…
Using the damped pendulum system we introduce the averaging method to study the periodic solutions of a dynamical system with small perturbation. We provide sufficient conditions for the existence of periodic solutions with small amplitude…
The aim of this article is to introduce an iterative algorithm for finding a common solution from the set of an equilibrium point for a bifunction and the set of a singularity of an inclusion problem on an Hadamard manifold. We also discuss…
Following Part~I, we consider a class of reversible systems and study bifurcations of homoclinic orbits to hyperbolic saddle equilibria. Here we concentrate on the case in which homoclinic orbits are symmetric, so that only one control…
Bifurcations associated with stability of the saddle fixed point of the Poincar\'{e} map, arising from the unstable equilibrium point of the potential, are investigated in a forced Duffing oscillator with a double-well potential. One…
Bipedal robots are essentially unstable because of their complex kinematics as well as high dimensional state space dynamics, hence control and generation of stable walking is a complex subject and still one of the active topics in the…
We investigate classical and semiclassical aspects of codimension--two bifurcations of periodic orbits in Hamiltonian systems. A classification of these bifurcations in autonomous systems with two degrees of freedom or time-periodic systems…
The Foucault Pendulum is a Spherical Pendulum of fixed length with two angular degrees of freedom, attached to a suspension which rotates once a day around the Earth axis at a distance essentially set by Earth radius and the geodetic…
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…
We investigate systems of equations, involving parameters from the point of view of both control theory and computer algebra. The equations might involve linear operators such as partial (q-)differentiation, (q-)shift, (q-)difference as…
The 1:1:2 resonant elastic pendulum is a simple classical system that displays the phenomenon known as Hamiltonian monodromy. With suitable initial conditions, the system oscillates between nearly pure springing and nearly pure…
This paper investigates the potential for stabilizing an inverted pendulum without electric devices, using gravitational potential energy. We propose a wheeled mechanism on a slope, specifically, a wheeled double pendulum, whose second…
A well-balanced second-order finite volume scheme is proposed and analyzed for a 2 X 2 system of non-linear partial differential equations which describes the dynamics of growing sandpiles created by a vertical source on a flat, bounded…
This article aims to answer the question, "What is the simplest system that embodies the essence of Foucault's pendulum?" We study a very elementary idealized system that exhibits a precession behavior analogous to the classic pendulum. The…
This study presents a study of equilibrium points, periodic orbits, stabilities, and manifolds in a rotating plane symmetric potential field. It has been found that the dynamical behaviour near equilibrium points is completely determined by…