Skip to content

Research at St Andrews

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).
Close

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
Publication statusPublished - Aug 2016

    Research areas

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

Discover related content
Find related publications, people, projects and more using interactive charts.

View graph of relations

Related by author

  1. On the regularity of the Green-Naghdi equations for a rotating shallow fluid layer

    Dritschel, D. G. & Jalali, M. R., 19 Feb 2019, In : Journal of Fluid Mechanics. 865, p. 100-136

    Research output: Contribution to journalArticle

  2. Scale-invariant singularity of the surface quasigeostrophic patch

    Scott, R. K. & Dritschel, D. G., 25 Mar 2019, In : Journal of Fluid Mechanics. 863, 12 p., R2.

    Research output: Contribution to journalArticle

  3. The stability and nonlinear evolution of quasi-geostrophic toroidal vortices

    Reinaud, J. N. & Dritschel, D. G., 25 Mar 2019, In : Journal of Fluid Mechanics. 863, p. 60-78

    Research output: Contribution to journalArticle

  4. Comparison of the Moist Parcel-in-Cell (MPIC) model with Large-Eddy Simulation for an idealised cloud

    Böing, S. J., Dritschel, D. G., Parker, D. J. & Blyth, A. M., 12 Mar 2019, (Accepted/In press) In : Quarterly Journal of the Royal Meteorological Society. In press

    Research output: Contribution to journalArticle

Related by journal

  1. Rigidity for sticky disks

    Connelly, R., Gortler, S. J. & Theran, L. S., 27 Feb 2019, In : Proceedings of the Royal Society A - Mathematical, Physical & Engineering Sciences. 475, 2222, 16 p., 20180773.

    Research output: Contribution to journalArticle

  2. Analytic analysis of auxetic metamaterials through analogy with rigid link systems

    Rayneau-Kirkhope, D., Zhang, C., Theran, L. S. & Dias, M., 21 Feb 2018, In : Proceedings of the Royal Society A - Mathematical, Physical & Engineering Sciences. 474, 2210, 12 p., 20170753.

    Research output: Contribution to journalArticle

  3. Stability analysis and simulations of coupled bulk-surface reaction-diffusion systems

    Madzvamuse, A., Chung, A. H. W. & Venkataraman, C., 8 Mar 2015, In : Proceedings of the Royal Society A - Mathematical, Physical & Engineering Sciences. 471, 2175, 18 p., 20140546.

    Research output: Contribution to journalArticle

  4. The motion of point vortices on closed surfaces

    Dritschel, D. G. & Boatto, S., 25 Feb 2015, In : Proceedings of the Royal Society A - Mathematical, Physical & Engineering Sciences. 471, 25 p., 20140890.

    Research output: Contribution to journalArticle

ID: 245112526