Volume 6, Issue 4, July 2018, Page: 85-88
Fractional Hamiltonian of Nonconservative Systems with Second Order Lagrangian
Ola Jarab'ah, Applied Physics Department, Faculty of Science, Tafila Technical University, Tafila, Jordan
Khaled Nawafleh, Department of Physics, Faculty of Science, Mu'tah University, AL-Karak, Jordan
Received: Jul. 5, 2018;       Accepted: Jul. 19, 2018;       Published: Aug. 24, 2018
DOI: 10.11648/j.ajpa.20180604.12      View  571      Downloads  53
Abstract
In this paper, the nonconservative systems with second order Lagrangian are investigated using fractional derivatives. The fractional Euler Lagrange equations for these systems are obtained. Then, fractional Hamiltonian for these systems is constructed, which is used to find the Hamilton's equations of motion in the same manner as those obtained by using the formulation of Euler Lagrange equations from variational problems, and it is observed that the Hamiltonian formulation is in exact agreement with the Lagrangian formulation. The passage from the Lagrangian containing fractional derivatives to the Hamiltonian is achieved. We have examined one example to illustrate the formalism.
Keywords
Fractional Derivatives, Lagrangian Formulation, Hamiltonian Formulation, Nonconservative Systems, Euler Lagrange Equations, Second Order Lagrangian
To cite this article
Ola Jarab'ah, Khaled Nawafleh, Fractional Hamiltonian of Nonconservative Systems with Second Order Lagrangian, American Journal of Physics and Applications. Vol. 6, No. 4, 2018, pp. 85-88. doi: 10.11648/j.ajpa.20180604.12
Copyright
Copyright © 2018 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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