Pragmatic Apparatus – A new pendulum motion with a suspended point near infinity

Cited by Lee Sonogan

Local geometry of the boundary Γ = ∂ Ω near infinity. | Download Scientific  Diagram

Abstract by A. I. Ismail 

In this paper, a pendulum model is represented by a mechanical system that consists of a simple pendulum suspended on a spring, which is permitted oscillations in a plane. The point of suspension moves in a circular path of the radius (a) which is sufficiently large. There are two degrees of freedom for describing the motion named; the angular displacement of the pendulum and the extension of the spring. The equations of motion in terms of the generalized coordinates φ and ξ are obtained using Lagrange’s equation. The approximated solutions of these equations are achieved up to the third order of approximation in terms of a large parameter ε will be defined instead of a small one in previous studies. The influences of parameters of the system on the motion are obtained using a computerized program. The computerized studies obtained show the accuracy of the used methods through graphical representations.

Publication: Scientific Reports (Peer-Reviewed Journal)

Pub Date: 24 June 2021 Doi: https://doi.org/10.1038/s41598-021-92646-6

Keywords: Applied mathematics, Applied physics, Mechanical engineering

https://www.nature.com/articles/s41598-021-92646-6#Sec6 (Plenty more sections, figures and references in this article)

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