Periodic Property and Instability of a Rotating Pendulum System
Ji‐Huan He, T. S. Amer, Shimaa Elnaggar, A. A. Galal
Abstract
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.
Topics & Concepts
PendulumPerturbation (astronomy)Nonlinear systemInstabilityClassical mechanicsMathematicsMotion (physics)Kapitza's pendulumProperty (philosophy)Mathematical analysisDouble pendulumDifferential equationInverted pendulumControl theory (sociology)PhysicsMechanicsComputer scienceArtificial intelligenceQuantum mechanicsControl (management)PhilosophyEpistemologyFractional Differential Equations SolutionsExperimental and Theoretical Physics StudiesModel Reduction and Neural Networks