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dc.contributor.advisorLeach, Peter Gavin Lawrence.
dc.creatorLemmer, Ryan Lee.
dc.date.accessioned2012-01-26T07:36:11Z
dc.date.available2012-01-26T07:36:11Z
dc.date.created1996
dc.date.issued1996
dc.identifier.urihttp://hdl.handle.net/10413/4899
dc.descriptionThesis (M.Sc.)-University of Natal, 1996.en
dc.description.abstractAn overview of the historical developments of the paradigms of classical mechanics, the free particle, oscillator and the Kepler problem, is given ito (in terms of) their conserved quantities. Next, the orbits of the three paradigms are found from quadratic forms. The quadratic forms are constructed using first integrals found by the application of Poisson's theorem. The orbits are presented ito expanding surfaces defined by the quadratic forms. The Lie and Noether symmetries of the paradigms are investigated. The free particle is discussed in detail and an overview of the work done on the oscillator and Kepler problem is given. The Lie and Noether theories are compared from various aspects. A technical description of Lie groups and algebras is given. This provides a basis for a discussion of the historical development of the paradigms of mechanics ito their group properties. Lastly the paradigms are discussed ito of Quantum Mechanics.en
dc.language.isoenen
dc.subjectDifferential equations, Linear.en
dc.subjectDifferential equations, Nonlinear.en
dc.subjectHarmonic analysis.en
dc.subjectLie groups.en
dc.subjectLie algebras.en
dc.subjectHamiltonian systems.en
dc.subjectTransformations (Mathematics)en
dc.subjectMechanics.en
dc.subjectTheses--Mathematics.en
dc.titleThe paradigms of mechanics : a symmetry based approach.en
dc.typeThesisen


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