The Motion of a Bead Sliding on a Wire in Fractional Sense

• Authors: D. Baleanu , A. Jajarmi , J. Asad , T. Blaszczyk
• Languages of publication: EN

Abstracts

EN

In this study, we consider the motion of a bead sliding on a wire which is bent into a parabola form. We first introduce the classical Lagrangian from the system model under consideration and obtain the classical Euler-Lagrange equation of motion. As the second step, we generalize the classical Lagrangian to the fractional form and derive the fractional Euler-Lagrange equation in terms of the Caputo fractional derivatives. Finally, we provide numerical solution of the latter equation for some fractional orders and initial conditions. The method we used is based on a discretization scheme using a Grünwald-Letnikov approximation for the fractional derivatives. Numerical simulations verify that the proposed approach is efficient and easy to implement.

Keywords

EN

motion of a bead on a wire; Euler-Lagrange equation; fractional derivative; Grünwald-Letnikov approximation

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2017
• Volume: 131
• Issue: 6
• Pages: 1561-1564

Dates

published

2017-06

received

2017-02-26

Contributors

author

D. Baleanu

• Department of Mathematics and Computer Science, Faculty of Arts and Sciences, Cankaya University, 06530 Ankara, Turkey
• Institute of Space Sciences, P.O. Box MG-23, 76900, Magurele, Bucharest, Romania

author

A. Jajarmi

• Department of Electrical Engineering, University of Bojnord, P.O. Box 94531-1339, Bojnord, Iran

author

J. Asad

• Department of Physics, College of Arts and Sciences, Palestine Technical University, P.O. Box 7, Tulkarm, Palestine

author

T. Blaszczyk

• Institute of Mathematics, Czestochowa University of Technology, al. Armii Krajowej 21, 42-201 Częstochowa, Poland

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Identifiers

DOI

10.12693/APhysPolA.131.1561