33 citations · 109 across the 9 of their papers we have counts for
9 papers
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…
The Chaplygin sleigh with friction moving due to periodic oscillations of an internal mass
Ivan A. Bizyaev, Alexey V. Borisov, Sergey P. Kuznetsov
For a Chaplygin sleigh moving in the presence of weak friction, we present and investigate two mechanisms of arising acceleration due to oscillations of an internal mass. In certai…
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…
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…
The Hess-Appelrot system and its nonholonomic analogs
Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev
This paper is concerned with the nonholonomic Suslov problem and its generalization proposed by Chaplygin. The issue of the existence of an invariant measure with singular density…
The Hojman Construction and Hamiltonization of Nonholonomic Systems
Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev
In this paper, using the Hojman construction, we give examples of various Poisson brackets which differ from those which are usually analyzed in Hamiltonian mechanics. They possess…
Figures of equilibrium of an inhomogeneous self-gravitating fluid
Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev
This paper is concerned with the figures of equilibrium of a self-gravitating ideal fluid with density stratification and a steady-state velocity field. As in the classical setting…
On the Routh sphere problem
I. A. Bizyaev, A. V. Tsiganov
We discuss an embedding of a vector field for the nonholonomic Routh sphere into a subgroup of commuting Hamiltonian vector fields on six dimensional phase space. The corresponding…