The Krylov–Bogoliubov–Mitropolsky method for modeling a forced damped quadratic pendulum oscillator

In the present investigation, a quadratically forced damped pendulum-type equation is solved analytically using several effective and highly accurate approaches. Some different types of pendulum oscillators linked to the forced and damped terms, in addition to the power of the damping term, are anal...

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Bibliographic Details
Published in:AIP advances 2023-08, Vol.13 (8), p.085029-085029-9
Main Authors: Alhejaili, Weaam, Salas, Alvaro H., El-Tantawy, S. A.
Format: Article
Language:English
Subjects:
Approximation
Damping
Error analysis
Oscillators
Pendulums
Runge-Kutta method
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Summary:In the present investigation, a quadratically forced damped pendulum-type equation is solved analytically using several effective and highly accurate approaches. Some different types of pendulum oscillators linked to the forced and damped terms, in addition to the power of the damping term, are analyzed. In the first part, the Krylov–Bogoliubov–Mitropolsky (KBM) technique and the ansatz method are carried out for analyzing the quadratically damped pendulum oscillator. In the second part, the two variants of the KBM technique are implemented for investigating the quadratically forced damped pendulum oscillator. Some symmetric approximations are derived and compared with the fourth-order Runge–Kutta numerical approximation. In addition, the maximum distance error is estimated in the whole study domain for ensuring that all obtained approximations are accurate. The obtained results are illustrated through concrete examples.
ISSN:2158-3226
2158-3226
DOI:10.1063/5.0159852