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

• Published in: Computer modeling in engineering & sciences Vol. 124; no. 3; pp. 953 - 968
• Main Authors: Baleanu, Dumitru, Ghanbari, Behzad, Asad, Jihad H., Jajarmi, Amin, Pirouz, Hassan Mohammadi
• Format: Journal Article
• Language: English
• Published: Tech Science Press 01.01.2020
• Subjects: Euler-Lagrange Equations; Fractional Derivative; Masses In Equilateral Triangle; Planar System; Springs
• ISSN: 1526-1492; 1526-1506
• DOI: 10.32604/cmes.2020.010236

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.