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http://hdl.handle.net/20.500.12358/21454
TitleConstrained Hamiltonian Systems with Higher-Order Lagrangians
Title in Arabicأنظمة هاملتون المقيدة للدوال اللاغرانجية ذوات الرتب العالية
Abstract

The higher-order regular Lagrangian is reduced to first-order singular Lagrangian. Dirac’s method of discrete regular systems with higher-order Lagrangian, are studied as singular systems with first-order Lagrangian, and the equations of motion are obtained. It is shown that the Hamilton-Jacobi approach leads to the same equations of motion as obtained by Dirac’s method. The second-order and third-order Lagrangian are studied as an examples. The Hamilton-Jacobi formulation for first-order constrained systems has been discussed. In such formalism the equations of motion are written as total differential equations in many variables. We generalize the Hamilton-Jacobi formulation for singular systems with second-order Lagrangians and apply this new formulation to Podolsky electrodynamics, comparing the results with the results obtained through Dirac’s method. The equations of motion for the associated Lagrangian to a nonholonomic Lagrangian of second-order are computed in both methods Dirac and Hamilton-Jacobi. Besides, the canonical path integral quantization was obtained to quantize singular systems. All the results obtained using Hamilton-Jacobi method, are in exact agreement with those results obtained using Dirac’s method.

Authors
Mahmoud, Sabreen Sobhy
Supervisors
Farhat, Nasser
Typeرسالة ماجستير
Date2015
LanguageEnglish
Publisherالجامعة الإسلامية - غزة
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  • PhD and MSc Theses- Faculty of Science [445]
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The institutional repository of the Islamic University of Gaza was established as part of the ROMOR project that has been co-funded with support from the European Commission under the ERASMUS + European programme. This publication reflects the views only of the author, and the Commission cannot be held responsible for any use which may be made of the information contained therein.

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The institutional repository of the Islamic University of Gaza was established as part of the ROMOR project that has been co-funded with support from the European Commission under the ERASMUS + European programme. This publication reflects the views only of the author, and the Commission cannot be held responsible for any use which may be made of the information contained therein.

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