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Point mass dynamics on spherical hyper-surfaces

Research output: Contribution to journalArticle

Abstract

The 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).
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Original languageEnglish
JournalPhilosophical Transactions of the Royal Society. A, Mathematical, Physical and Engineering Sciences
DOIs
Publication statusAccepted/In press - 15 Apr 2019

    Research areas

  • Hamiltonian dynamics, Surfaces, Gravity

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