Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/3848
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dc.contributor.advisorPashaev, Oktay-
dc.contributor.authorTığrak Ulaş, Esra-
dc.date.accessioned2014-07-22T13:52:30Z-
dc.date.available2014-07-22T13:52:30Z-
dc.date.issued2007-
dc.identifier.urihttp://hdl.handle.net/11147/3848-
dc.descriptionThesis (master)--Izmir Institute of Technology, Mathematics, Izmir, 2007en_US
dc.descriptionIncludes bibliographical references (leaves: 149-151)en_US
dc.descriptionText in English; Abstract: Turkish and Englishen_US
dc.descriptionxi, 175 leavesen_US
dc.description.abstractIn my thesis we have studied the universe models as dynamical systems which can be represented by harmonic oscillators. For example, a harmonic oscillatior equation is constructed by the transformation of the Riccati differential equations for the anisotropic and homogeneous metric. The solution of the Friedman equations with the state equation satisfies both bosonic expansion and fermionic contraction in Friedman Robertson Walker universe with different curvatures is studied as a conservative system with the harmonic oscillator equations. Apart from the oscillator representations mentioned above (constructed from the universe models), we showed that the linearization of the Einstein field equations produces harmonic oscillator equation with constant frequency and the linearization of the metric on the de-Sitter background produces damped harmonic oscillator system. In addition to these, we have constructed the doublet and the Caldirola type oscillator equations with time dependent damping and frequency terms in the light of the Sturm Liouville form. The Lagrangian and Hamiltonian functions are calculated for all particular cases of the Sturm Liouville form. Finally, we have shown that zeros of the oscillator equations constructed from the particular cases can be transformed into pole singularities of the Riccati equations.en_US
dc.language.isoenen_US
dc.publisherIzmir Institute of Technologyen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subject.lccQC125.2 T56 2007en
dc.subject.lcshHarmonic ascillatorsen
dc.subject.lcshGeneal relativity (Physics)en
dc.subject.lcshRiccati equationsen
dc.subject.lcshDifferential equationsen
dc.titleDamping Oscillatory Models in General Theory of Relativityen_US
dc.typeMaster Thesisen_US
dc.institutionauthorTığrak Ulaş, Esra-
dc.departmentThesis (Master)--İzmir Institute of Technology, Mathematicsen_US
dc.relation.publicationcategoryTezen_US
dc.identifier.wosqualityN/A-
dc.identifier.scopusqualityN/A-
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
item.languageiso639-1en-
item.openairetypeMaster Thesis-
item.grantfulltextopen-
item.fulltextWith Fulltext-
item.cerifentitytypePublications-
Appears in Collections:Master Degree / Yüksek Lisans Tezleri
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