Regular and Chaotic Dynamics

, Volume 15, Issue 4–5, pp 440–461 | Cite as

Coupled motion of a rigid body and point vortices on a two-dimensional spherical surface

Special Issue: Valery Vasilievich Kozlov-60

Abstract

The paper is concerned with a class of problems which involves the dynamical interaction of a rigid body with point vortices on the surface of a two-dimensional sphere. The general approach to the 2D hydrodynamics is further developed. The problem of motion of a dynamically symmetric circular body interacting with a single vortex is shown to be integrable. Mass vortices on S2 are introduced and the related issues (such as equations of motion, integrability, partial solutions, etc.) are discussed. This paper is a natural progression of the author’s previous research on interaction of rigid bodies and point vortices in a plane.

Key words

hydrodynamics on a sphere coupled body-vortex system mass vortex equations of motion integrability 

MSC2000 numbers

76B47 70Exx 70Hxx 

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Copyright information

© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  • A. V. Borisov
    • 1
  • I. S. Mamaev
    • 1
  • S. M. Ramodanov
    • 1
  1. 1.Institute of Computer ScienceIzhevskRussia

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