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Title: Classical and fractional aspects of two coupled pendulums
Authors: Baleanu, D
Jajarmi, A
Asad, J. H
Keywords: Two coupled pendulums;Euler-Lagrange equation;fractional derivative;Euler method.
Issue Date: 2019
Publisher: Editura Academiei Romane/Publishing House of the Romanian Academy
Citation: Baleanu, D., Jajarmi, A., Asad, J.H. (2019). Classical and fractional aspects of two coupled pendulums. Romanian Reports in Physics 71(1),103
Abstract: In this study, we consider two coupled pendulums (attached together with a spring) having the same length while the same masses are attached at their ends. After setting the system in motion we construct the classical Lagrangian, and as a result, we obtain the classical Euler-Lagrange equation. Then, we generalize the classical Lagrangian in order to derive the fractional Euler-Lagrange equation in the sense of two different fractional operators. Finally, we provide the numerical solution of the latter equation for some fractional orders and initial conditions. The method we used is based on the Euler method to discretize the convolution integral. Numerical simulations show that the proposed approach is efficient and demonstrate new aspects of the real-world phenomena.
ISSN: 12211451
Appears in Collections:Applied science faculty

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