Related papers: The Spherical Kapitza-Whitney Pendulum

A double pendulum subject to external torques is used as a model to study the stability of a planar manipulator with two links and two rotational driven joints. The hamiltonian equations of motion and the fixed points (stationary solutions)…

A thin and narrow rectangular plate having the two short edges hinged and the two long edges free is considered. A nonlinear nonlocal evolution equation describing the deformation of the plate is introduced: well-posedness and existence of…

Interfacial instability would be aroused on a spherical liquid droplet when it is subject to external vertical vibration. In this paper, a linear analysis was conducted on this instability problem. The polar-angle dependent acceleration in…

We present an experimental setup to demonstrate normal modes and symmetry breaking in a two-dimensional pendulum. In our experiment we have used two modes of a single oscillator to demonstrate normal modes, as opposed to two single…

We prove that the Ziegler pendulum -- a double pendulum with a follower force -- can be integrable, provided that the stiffness of the elastic spring located at the pivot point of the pendulum is zero and there is no friction in the system.…

The author considers the planar rotational motion of the mathematical pendulum with its pivot oscillating both vertically and horizontally, so the trajectory of the pivot is an ellipse close to a circle. The analysis is based on the exact…

A popular model for a generic fat-cored vortex ring or eddy is Hill's spherical vortex (Phil. Trans. Roy. Soc. A vol. 185, 1894, p. 213). Here we find an exact solution for such a spherical vortex steadily propagating along the axis of a…

We study the existence of asymptotically stable periodic trajectories induced by reset feedback. The analysis is developed for a planar system. Casting the problem into the hybrid setting, we show that a periodic orbit arises from the…

We extend the theory of Kapitza stabilization within the complex domain, i.e. for the case of an imaginary oscillating potential. At a high oscillation frequency, the quasi-energy spectrum is found to be entirely real-valued, however a…

We discuss the equation of motion of the driven pendulum and generalize it to arbitrary driving angle. The pendulum will oscillate about a stable angle other than straight down if the drive amplitude and frequency are large enough for a…

In this paper we study a Fermi-Ulam model where a pingpong bounces elastically against a periodically oscillating platform in a gravity field. We assume that the platform motion $f(t)$ is piecewise $C^3$ with a singularity…

In the present paper, the nonlinear differential equation of pendulum is investigated to find an exact closed form solution, satisfying governing equation as well as initial conditions. The new concepts used in the suggested method are…

The dynamics of two planar elastic pendula mounted on the horizontally excited platform have been studied. We give evidence that the pendula can exhibit synchronous oscillatory and rotation motion and show that stable in-phase and…

The quantum states of the Kapitza pendulum are described within the effective potential obtained by the method of averaging over the fast oscillations. An analytical estimate of the energy spectrum of stabilized states is given using…

In this paper we study an optimal control problem that is affine in two-dimensional bounded control. The problem is related to the stabilization of an inverted spherical pendulum in the vicinity of the upper unstable equilibrium. We find…

The behavior of a stationary inverted point mass pendulum pivoted at its lower end in a gravitational potential is studied under the influence of statistical fluctuations. It is shown using purely classical equations that the pendulum…

We study effects of a rippling gravitational background on a scalar field with a double well potential, focusing on the analogy with the well known dynamics of the Kapitza's pendulum. The ripples are rendered as infinitesimal but rapidly…

We study the dynamics of $N$ point vortices on a rotating sphere. The Hamiltonian system becomes infinite dimensional due to the non-uniform background vorticity coming from the Coriolis force. We prove that a relative equilibrium formed of…

We develop a contraction-based framework to establish the existence and exponential stability of periodic solutions in planar nonsmooth dynamical systems governed by Filippov differential inclusions. The method integrates a time- and…

We identify the nonlinear normal modes spawning from the stable equilibrium of a double pendulum under gravity, and we establish their connection to homoclinic orbits through the unstable upright position as energy increases. This result is…