Related papers: The Inverted Pendulum as a Classical Analog of the…
The quantum effective action may be used to invert information from phenomena, either measured or ideal, to the microscopic Lagrangian. As an example of this procedure the lattice composition of a solid can be determined in principle from…
The small angle approximation often fails to explain experimental data, does not even predict if a plane pendulum's period increases or decreases with increasing amplitude. We make a perturbation ansatz for the Conserved Energy Surfaces of…
Using tools and techniques from geometric control theory, namely Hermann-Nagano theorem, we prove controllability result for a mechanical system consisting of a planar double inverted pendulum fixed to a wheeled cart that can move linearly…
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…
In this paper, a novel recurrent adaptive backstepping optimal control strategy for a single inverted pendulum system is studied. By this method, an inverted pendulum is stabilized using projection recurrent neural network-based adaptive…
In the paper we consider systems in oscillating force fields such that the classical method of averaging can be applied. We present sufficient conditions for the existence of forced oscillations in such systems and study the asymptotic…
The model we consider consists in a double pendulum set, where the pivot points are free to shift along a horizontal line. Moreover, the two pendula are coupled by means of a spring whose extremities connect two points of each pendulum, at…
For the system of an inverted spherical pendulum with friction and a periodically moving pivot point we prove the existence of at least one periodic solution with the additional property of being falling-free. The last means that the…
In this work, an intelligent controller is employed to the chaos control problem in a nonlinear pendulum. The adopted approach is based on the sliding mode control strategy and enhanced by an adaptive fuzzy algorithm to cope with modeling…
A unified, consistent and simple view of the Faraday law of induction is presented, which consists of two points: discriminating the lab- from the rest-frame electric field and understanding it is the impossibility for both fields to vanish…
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…
The normal and the inverted pendulum continue to be one of the main physical models and metaphors in science. The inverted pendulum is also a classic study case in control theory. In this paper we consider a special demonstration version of…
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…
In this paper we explore the stability of an inverted pendulum with generalized parametric excitation described by a superposition of $N$ sines with different frequencies and phases. We show that when the amplitude is scaled with the…
The article provides the formula for the calculation the falling time of inverted pendulum. The result is expressed in terms of elliptic integrals of first kind. The asymptotic formula for small initial inclination value is also provided.
A toroidal trap combined with external time-dependent electric field can be used for implementing different dynamical regimes of matter waves. In particular, we show that dynamical and stochastic acceleration, localization and…
One of the many surprising results found in the mechanics of rotating systems is the stabilization of a particle in a rapidly rotating planar saddle potential. Besides the counterintuitive stabilization, an unexpected precessional motion is…
We study dynamics of the inverted pendulum on the wheel on a soft surface and under a proportional-integral-derivative controller. The behaviour of such pendulum is modelled by a system with a differential inclusion. If the the system has a…
The purpose of this article is to illustrate the role of connections and symmetries in the Wheeled Inverted Pendulum (WIP) mechanism - an underactuated system with rolling constraints - popularized commercially as the Segway, and thereby…
The counter-intuitive rotational motion of the propeller of a devil's stick when the agitator is rubbed against the pylon has long intrigued performers, audiences and scientists. The apparently unrelated phenomenon of self-stabilization of…