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N-body dynamics on closed surfaces: the axioms of mechanics

Research output: Contribution to journalArticle

Author(s)

Stefanella Boatto, David Gerard Dritschel, Rodrigo G Schaefer

School/Research organisations

Abstract

A major challenge for our understanding of the mathematical basis of particle dynamics is the formulation of N-body and N-vortex dynamics on Riemann surfaces. In this paper, we show how the two problems are, in fact, closely related when considering the role played by the intrinsic geometry of the surface. This enables a straightforward deduction of the dynamics of point masses, using recently derived results for point vortices on general closed differentiable surfaces M endowed with a metric g. We find, generally, that Kepler's Laws do not hold. What is more, even Newton's First Law (the law of inertia) fails on closed surfaces with variable curvature (e.g. the ellipsoid).
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Details

Original languageEnglish
Article number20160020
Number of pages20
JournalProceedings of the Royal Society A - Mathematical, Physical & Engineering Sciences
Volume472
Issue number2192
Early online date10 Aug 2016
DOIs
StatePublished - Aug 2016

    Research areas

  • N-body problem, Point-vortex dynamics, Hamiltonian systems, Newton's Laws, Surfaces of revolution, Equivalence principle

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