dc.contributor.author Armstrong, Craig Keith en_NZ dc.date.accessioned 2007-03-01T11:40:24Z dc.date.available 2007-07-26T10:48:17Z dc.date.issued 2007 en_NZ dc.identifier.citation Armstrong, C. K. (2007). Hamilton-Jacobi Theory and Superintegrable Systems (Thesis, Master of Science (MSc)). The University of Waikato, Hamilton, New Zealand. Retrieved from https://hdl.handle.net/10289/2340 en dc.identifier.uri https://hdl.handle.net/10289/2340 dc.description.abstract Hamilton-Jacobi theory provides a powerful method for extracting the equations of motion out of some given systems in classical mechanics. On occasion it allows some systems to be solved by the method of separation of variables. If a system with n degrees of freedom has 2n - 1 constants of the motion that are polynomial in the momenta, then that system is called superintegrable. Such a system can usually be solved in multiple coordinate systems if the constants of the motion are quadratic in the momenta. All superintegrable two dimensional Hamiltonians of the form H = (p_x)sup2 + (p_y)sup2 + V(x,y), with constants that are quadratic in the momenta were classified by Kalnins et al [5], and the coordinate systems in which they separate were found. en_NZ We discuss Hamilton-Jacobi theory and its development from a classical viewpoint, as well as superintegrability. We then proceed to use the theory to find equations of motion for some of the superintegrable Hamiltonians from Kalnins et al [5]. We also discuss some of the properties of the Poisson algebra of those systems, and examine the orbits. dc.format.mimetype application/pdf dc.language.iso en dc.publisher The University of Waikato en_NZ dc.rights All items in Research Commons are provided for private study and research purposes and are protected by copyright with all rights reserved unless otherwise indicated. dc.subject Hamilton-Jacobi theory en_NZ dc.subject superintegrability en_NZ dc.subject superintegrable systems en_NZ dc.subject Hamiltonian en_NZ dc.subject canonical transformations en_NZ dc.subject classical mechanics en_NZ dc.subject Lagrangian mechanics en_NZ dc.subject Hamiltonian mechanics en_NZ dc.subject two-dimensional Kepler problem en_NZ dc.subject two-dimensional harmonic oscillator en_NZ dc.title Hamilton-Jacobi Theory and Superintegrable Systems en_NZ dc.type Thesis en_NZ thesis.degree.discipline Computing and Mathematical Sciences en_NZ thesis.degree.grantor University of Waikato en_NZ thesis.degree.level Masters thesis.degree.name Master of Science (MSc) en_NZ uow.date.accession 2007-03-01T11:40:24Z en_NZ uow.date.available 2007-07-26T10:48:17Z en_NZ uow.identifier.adt http://adt.waikato.ac.nz/public/adt-uow20070301.114024 en_NZ uow.date.migrated 2009-06-09T23:29:31Z en_NZ pubs.place-of-publication Hamilton, New Zealand en_NZ
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