article · Axioms
This study investigates the dynamical behaviour of a pendulum attached to a rigid frame that rotates with a constant angular velocity about a vertical axis passing through the pivot point. To analyse the system, He's homotopy perturbation method is applied to derive an analytical solution for the governing non-linear differential equation of motion. The precision of this analytical result is verified by comparing it against numerical results from the fourth-order Runge-Kutta method as well as He's frequency formulation. Furthermore, the conditions required for stable motion are examined and detailed. Graphical plots of the time histories are provided to demonstrate how variations in different physical parameters directly influence the overall dynamical response and stability of the rotating pendulum system.
Understanding non-linear dynamics in rotating systems is fundamental to predicting how mechanical structures behave under continuous rotational forces. By providing verified analytical solutions and defining stability conditions, this work deepens theoretical insights into oscillatory mechanics, helping researchers understand how alterations in physical parameters can prevent or trigger instability in rotating assemblies.
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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.
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DOI: 10.3390/axioms10030191
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