69 citations · 642 across the 30 of their papers we have counts for
32 papers
Circular orbits of a ball on a rotating conical turntable
Alexey V. Borisov, Tatiana B. Ivanova, Alexander A. Kilin +1
This paper is concerned with the study of the rolling without slipping of a dynamically symmetric (in particular, homogeneous) heavy ball on a cone which rotates uniformly about it…
Dynamics of the Chaplygin ball on a rotating plane
Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev
This paper addresses the problem of the Chaplygin ball rolling on a horizontal plane which rotates with constant angular velocity. In this case, the equations of motion admit area…
Fermi-like acceleration and power-law energy growth in nonholonomic systems
Ivan . A. Bizyaev, Alexey V. Borisov, Valery V. Kozlov +1
This paper is concerned with a nonholonomic system with parametric excitation - the Chaplygin sleigh with time-varying mass distribution. A detailed analysis is made of the problem…
The Chaplygin sleigh with parametric excitation: chaotic dynamics and nonholonomic acceleration
Ivan Bizyaev, Alexey Borisov, Ivan Mamaev
This paper is concerned with the Chaplygin sleigh with timevarying mass distribution (parametric excitation). The focus is on the case where excitation is induced by a material poi…
Reduction and relative equilibria for the 2-body problem in spaces of constant curvature
A. V. Borisov, L. C. García-Naranjo, I. S. Mamaev +1
We consider the two-body problem on surfaces of constant non-zero curvature and classify the relative equilibria and their stability. On the hyperbolic plane, for each q>0 we show…
Generalizations of the Kovalevskaya case and quaternions
Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev
This paper provides a detailed description of various reduction schemes in rigid body dynamics. Analysis of one of such nontrivial reductions makes it possible to order the cases a…