Planar System-Masses in an Equilateral Triangle: Numerical Study within Fractional Calculus
- Dumitru Baleanu1,2, Behzad Ghanbari3, Jihad H. Asad4,*, 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:
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:
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.
Keywords
Planar system; masses in equilateral triangle; springs; Euler-Lagrange equations; fractional derivative
Cite This Article
Baleanu, D., Ghanbari, B., Asad, J. H., Jajarmi, A., Pirouz, H. M. (2020). Planar System-Masses in an Equilateral Triangle: Numerical Study within Fractional Calculus. CMES-Computer Modeling in Engineering & Sciences, 124(3), 953–968.
This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.