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dc.contributor.authorDritschel, David Gerard
dc.identifier.citationDritschel , D G 2019 , ' Point mass dynamics on spherical hypersurfaces ' , Philosophical Transactions of the Royal Society. A, Mathematical, Physical and Engineering Sciences , vol. 377 , no. 2158 , 20180349 , pp. 1-11 .
dc.identifier.otherPURE: 258701266
dc.identifier.otherPURE UUID: e1e0df46-f944-41f4-96f4-f0d25890fdf3
dc.identifier.otherORCID: /0000-0001-6489-3395/work/64697793
dc.identifier.otherScopus: 85073197475
dc.identifier.otherWOS: 000488279300004
dc.description.abstractThe equations of motion are derived for a system of point masses on the (hyper-)surface Sn of a sphere embedded in ℝn+1 for any dimension n > 1. Due to the symmetry of the surface, the equations take a particularly simple form when using the Cartesian coordinates of ℝn+1. The constraint that the distance of the jth mass‖rj‖ from the origin remains constant (i.e. each mass remains on the surface) is automatically satisfied by the equations of motion. Moreover, the equations are a Hamiltonian system with a conserved energy as well as a host of conserved angular momenta. Several examples are illustrated in dimensions n = 2 (the sphere) and n= 3 (the glome).
dc.relation.ispartofPhilosophical Transactions of the Royal Society. A, Mathematical, Physical and Engineering Sciencesen
dc.rights© The Authors 2019. This work has been made available online in accordance with the publisher's policies. This is the author created accepted version manuscript following peer review and as such may differ slightly from the final published version. The final published version of this work is available at
dc.subjectHamiltonian dynamicsen
dc.subjectQA Mathematicsen
dc.subjectQC Physicsen
dc.titlePoint mass dynamics on spherical hypersurfacesen
dc.typeJournal articleen
dc.contributor.institutionUniversity of St Andrews.Marine Alliance for Science & Technology Scotlanden
dc.contributor.institutionUniversity of St Andrews.Scottish Oceans Instituteen
dc.contributor.institutionUniversity of St Andrews.Applied Mathematicsen
dc.description.statusPeer revieweden

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