TY - EJOU
AU - Baleanu, Dumitru
AU - Ghanbari, Behzad
AU - Asad, Jihad H.
AU - Jajarmi, Amin
AU - Pirouz, Hassan Mohammadi
TI - Planar System-Masses in an Equilateral Triangle: Numerical Study within Fractional Calculus
T2 - Computer Modeling in Engineering \& Sciences
PY - 2020
VL - 124
IS - 3
SN - 1526-1506
AB - 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.
KW - Planar system; masses in equilateral triangle; springs; Euler-Lagrange equations; fractional derivative
DO - 10.32604/cmes.2020.010236