Dynamics of a DC Motor-Driving Arm with a Circular Periodic Potential and DC/AC Voltage Input

Abstract

In this paper, we investigate the dynamics of an electromechanical system consisting of a DC motor-driving arm within a circular periodic potential created by three permanent magnets. Two configurations of the circular potential appear when one varies the positions of the magnets and the length of the DC motor, respectively. Two different forms of input signal are used: DC and AC voltage sources. For each case, conditions under which the mechanical arm can perform a complete rotation are obtained. Under the DC voltage excitation, the arm oscillates and then is stabilized at an equilibrium position for a DC voltage lower than a critical value [Formula: see text]. When the DC voltage is higher than the critical value [Formula: see text], the arm performs large amplitude motions (complete rotation). Submitted to an AC voltage with amplitude lower than a critical value, the mechanical arm exhibits sinusoidal oscillations around the equilibrium position [Formula: see text] with amplitudes less than one turn. Angular oscillations with amplitudes greater than one turn are observed when the voltage amplitude is higher than the critical value. Bifurcation diagrams show that the simple system can enter chaotic regime with the amplitudes of angular oscillations varying erratically from small to high values.