Coupled motion of a rigid body and point vortices on a sphere

    2009, Vol. 5, No. 3, pp.  319-343

    Author(s): Borisov A. V., Mamaev I. S., Ramodanov S. M.

    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 $S^2$ 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.
    Keywords: hydrodynamics on a sphere, coupled body-vortex system, mass vortex, equations of motion, integrability
    Citation: Borisov A. V., Mamaev I. S., Ramodanov S. M., Coupled motion of a rigid body and point vortices on a sphere, Rus. J. Nonlin. Dyn., 2009, Vol. 5, No. 3, pp.  319-343

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