69 citations · 132 across the 5 of their papers we have counts for
5 papers
New periodic solutions for three or four identical vortices on a plane and a sphere
A. V. Borisov, I. S. Mamaev, A. A. Kilin
In this paper we describe new classes of periodic solutions for point vortices on a plane and a sphere. They correspond to similar solutions (so-called choreographies) in celestial…
Reduction and chaotic behavior of point vortices on a plane and a sphere
A. V. Borisov, A. A. Kilin, I. S. Mamaev
We offer a new method of reduction for a system of point vortices on a plane and a sphere. This method is similar to the classical node elimination procedure. However, as applied t…
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…
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.…
The Rolling Motion of a Ball on a Surface. New Integrals and Hierarchy of Dynamics
A. V. Borisov, I. S. Mamaev, A. A. Kilin
The paper is concerned with the problem on rolling of a homogeneous ball on an arbitrary surface. New cases when the problem is solved by quadratures are presented. The paper also…