Symplectic integrators for vakonomic equations and for multi-Hamiltonian equations : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Mathematics at Massey University, Palmerston North, New Zealand

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dc.contributor.authorWilkins, Matthew Colin
dc.date.accessioned2016-08-18T01:04:19Z
dc.date.available2016-08-18T01:04:19Z
dc.date.issued2016
dc.descriptionListed in 2016 Dean's List of Exceptional Thesesen
dc.description.abstractAlmost 200 years ago William Hamilton gave the world his reformulation of classical mechanics: the so-called Hamiltonian mechanics. By permitting a singular structure matrix, Mr Wilkins’ research extended this exalted theory to accommodate the Vakonomic equations, consequently allowing a solution to the sub-Riemannian geodesic and optimal control problems within this framework. The multi-Hamiltonian equation is an extension of Hamiltonian mechanics that appears in fields ranging from quantum mechanics to classical electrodynamics. Mr Wilkins’ research was conducted to the highest standards using numerical and theoretical proof and provided a stable, high-order multisymplectic numerical method for solving the multi-Hamiltonian equations where none previously existed. Our knowledge has increased because Hamiltonian mechanics has been extended to accommodate the Vakonomic equations and humanity now has a high-order multisymplectic numerical method for solving multi-Hamiltonian equations.en_US
dc.identifier.urihttp://hdl.handle.net/10179/8537
dc.language.isoenen_US
dc.publisherMassey Universityen_US
dc.rightsThe Authoren_US
dc.subjectHamiltonian systemsen_US
dc.subjectDifferential equationsen_US
dc.subjectDifferential equations, Partialen_US
dc.subjectDean's List of Exceptional Thesesen
dc.titleSymplectic integrators for vakonomic equations and for multi-Hamiltonian equations : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Mathematics at Massey University, Palmerston North, New Zealanden_US
dc.typeThesisen_US
massey.contributor.authorWilkins, Matthew Colinen_US
thesis.degree.disciplineMathematicsen_US
thesis.degree.grantorMassey Universityen_US
thesis.degree.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophy (Ph.D.)en_US
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