69 citations · 763 across the 42 of their papers we have counts for
44 papers
On inhomogeneous nonholonomic Bilimovich system
A. V. Borisov, E. A. Mikishanina, A. V. Tsiganov
We consider a simple motivating example of a non-Hamiltonian dynamical system with time-dependent constraints obtained by imposing rheonomic non-integrable Bilimovich's constraint…
On rheonomic nonholonomic deformations of the Euler equations proposed by Bilimovich
A. V. Borisov, A. V. Tsiganov
In 1913 A.D. Bilimovich observed that rheonomic linear and homogeneous in generalized velocities constraints are ideal. As a typical example, he considered rheonomic nonholonomic d…
On the Chaplygin sphere in a magnetic field
A. V. Borisov A. V. Tsiganov
We consider the possibility of using Dirac's ideas of the deformation of Poisson brackets in nonholonomic mechanics. As an example, we analyze the composition of external forces th…
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…
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…