Open Access

ARTICLE

Planar System-Masses in an Equilateral Triangle: Numerical Study within Fractional Calculus

Dumitru Baleanu^1,2, Behzad Ghanbari³, Jihad H. Asad^4,*, Amin Jajarmi⁵, Hassan Mohammadi Pirouz⁵
1 Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, Ankara, 06530, Turkey
2 Institute of Space Sciences, Bucharest, 76900, Romania
3 Department of Engineering Science, Kermanshah University of Technology, Kermanshah, Iran
4 Department of Physics, College of Arts and Sciences, Palestine Technical University, Tulkarm, Palestine
5 Department of Electrical Engineering, University of Bojnord, Bojnord, Iran
* Corresponding Author: Jihad H. Asad. Email:

Computer Modeling in Engineering & Sciences 2020, 124(3), 953-968. https://doi.org/10.32604/cmes.2020.010236

Received 19 February 2020; Accepted 16 June 2020; Issue published 21 August 2020

Abstract

In this work, a system of three masses on the vertices of equilateral triangle is investigated. This system is known in the literature as a planar system. We first give a description to the system by constructing its classical Lagrangian. Secondly, the classical Euler-Lagrange equations (i.e., the classical equations of motion) are derived. Thirdly, we fractionalize the classical Lagrangian of the system, and as a result, we obtain the fractional Euler-Lagrange equations. As the final step, we give the numerical simulations of the fractional model, a new model which is based on Caputo fractional derivative.

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Keywords

Planar system; masses in equilateral triangle; springs; Euler-Lagrange equations; fractional derivative

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Citations