58 citations · 188 across the 7 of their papers we have counts for
7 papers
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…
On the History of the Development of the Nonholonomic Dynamics
A. V. Borisov, I. S. Mamaev
The main directions in the development of the nonholonomic dynamics are briefly considered in this paper. The first direction is connected with the general formalizm of the equatio…
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.…
Integrability of the problem of motion of a cylinder and a point vortex in a perfect fluid
A. V. Borisov, I. S. Mamaev
Motion of a cylinder dynamically interacting with n point vortices in a perfect fluid is considered. A nonliniear Poisson structure and two integrals of motion are found. The equat…
Euler-Poisson Equations and Integrable Cases
A. V. Borisov, I. S. Mamaev
In this paper we propose a new approach to the study of integrable cases based on intensive computer methods' application. We make a new investigation of Kovalevskaya and Goryachev…
Motion of a circular cylinder and n point vortices in a perfect fluid
A. V. Borisov, I. S. Mamaev, S. M. Ramodanov
The paper studies the system of a rigid body interacting dynamically with point vortices in a perfect fluid. For arbitrary value of vortex strengths and circulation around the cyli…