Periodic Property and Instability of a Rotating Pendulum System

The current paper investigates the dynamical property of a pendulum attached to a rotating rigid frame with a constant angular velocity about the vertical axis passing to the pivot point of the pendulum. He's homotopy perturbation method is used to obtain the analytic solution of the governing nonlinear differential equation of motion. The fourth-order Runge-Kutta method (RKM) and He's frequency formulation are used to verify the high accuracy of the obtained solution. The stability condition of the motion is examined and discussed. Some plots of the time histories of the gained solutions are portrayed graphically to reveal the impact of the distinct parameters on the dynamical motion.

Automated summary

This paper investigates the dynamical properties of a pendulum attached to a rotating rigid frame with a constant angular velocity. The analytic solution of the governing nonlinear differential equation of motion is obtained using He's homotopy perturbation method. The obtained solution is verified for high accuracy using the fourth-order Runge-Kutta method and He's frequency formulation. The stability condition of the motion is examined and discussed, and the impact of different parameters on the dynamical motion is revealed through graphical representations of time histories.