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 indicates a specialâ€¦ (More)

In this paper we consider cases of existence of invariant measure, additional first integrals, and Poisson structure in a problem of rigid bodyâ€™s rolling without sliding on plane and sphere. Theâ€¦ (More)

We perform the bifurcation analysis of the Kepler problem on S and L. An analogue of the Delaunay variables is introduced. We investigate the motion of a point mass in the field of the Newtonianâ€¦ (More)

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 cylinder the system isâ€¦ (More)

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. Appel and D.â€¦ (More)

We consider Chaplygin's equations [Izd. Akad. Nauk SSSR 3, 3 (1933)] describing the planar motion of a rigid body in an unbounded volume of an ideal fluid while circulation around the body is notâ€¦ (More)

We consider integrable spherical analogue of the Darboux potential, which appear in the problem (and its generalizations) of the planar motion of a particle in the field of two and four fixedâ€¦ (More)

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 mechanics .

This paper is concerned with the problem of a rigid body (tripod) moving with three points in contact with a horizontal plane under the action of dry friction forces. It is shown that the regime ofâ€¦ (More)

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 to the vortexâ€¦ (More)