Analytical and numerical study of a vibrating magnetic inverted pendulum

Abstract The current study investigates the stability structure of base periodic motion an inverted pendulum (IP). A uniform magnetic field affects in direction plane configuration. Furthermore, a non-conservative force as one that dampens air is considered. Its underlying equation derived from traditional analytical mechanics. mathematical analysis made simpler by substituting Taylor theory order to expand restoring forces. modified Homotopy perturbation method (HPM) employed achieve roughly adequate regular result. To support prior result, numerical based on fourth-order Runge-Kutta (RK4) employed. graphs for both analytic and solutions are highly consistent with another, which indicates strategy accurate. solution time history curve exhibits decaying performance it steady without chaos. resonance non-resonance cases found through using scale method. In all approaches, methodology multiple scales actually regarded further standard approach. used create collection graphs. Some graphical representations illustrate how typical physical values affect behavior discovered solution. It has been statically unstable IP can have its instability reduced raising spring torsional constant stiffness well damped coefficient. Moreover, significant role configuration, explains at higher this field, waves take much more than smaller field. Accordingly, be various engineering devices need certain period stable.