69 citations · 394 across the 20 of their papers we have counts for
9 papers · 1 filter
Stability of Thomson's Configurations of Vortices on a Sphere
A. V. Borisov, A. A. Kilin
In this work stability of polygonal configurations on a plane and sphere is investigated. The conditions of linear stability are obtained. A nonlinear analysis of the problem is ma…
Lie algebras in vortex dynamics and celestial mechanics - IV
A. V. Bolsinov, A. V. Borisov, I. S. Mamaev
The work of A.V. Borisov, A.E. Pavlov, Dynamics and Statics of Vortices on a Plane and a Sphere - I (Reg. & Ch. Dynamics, 1998, Vol. 3, No 1, p.28-39) introduces a naive descriptio…
Dynamics of three vortices on a plane and a sphere -- III. Noncompact case. Problems of collaps and scattering
A. V. Borisov, V. G. Lebedev
In this article we considered the integrable problems of three vortices on a plane and sphere for noncompact case. We investigated explicitly the problems of a collapse and a scatt…
Dynamics of three vortices on a plane and a sphere - II. General compact case
A. V. Borisov, V. G. Lebedev
Integrable problem of three vorteces on a plane and sphere are considered. The classification of Poisson structures is carried out. We accomplish the bifurcational analysis using t…
Dynamics and statics of vortices on a plane and a sphere - I
A. V. Borisov, A. E. Pavlov
In the present paper a description of a problem of point vortices on a plane and a sphere in the "internal" variables is discussed. The hamiltonian equations of motion of vortices…
Dynamics of rolling disk
A. V. Borisov, I. S. Mamaev, A. A. Kilin
In the paper we present the qualitative analysis of rolling motion without slipping of a homogeneous round disk on a horisontal plane. The problem was studied by S.A. Chaplygin, P.…