Elizaveta Artemova
Publications:
Artemova E. M., Kilin A. A.
Dynamics of Two Vortex Rings in a Bose – Einstein Condensate
2022, vol. 27, no. 6, pp. 713732
Abstract
In this paper, we consider the dynamics of two interacting point vortex rings in
a Bose – Einstein condensate. The existence of an invariant manifold corresponding to vortex
rings is proved. Equations of motion on this invariant manifold are obtained for an arbitrary
number of rings from an arbitrary number of vortices. A detailed analysis is made of the case
of two vortex rings each of which consists of two point vortices where all vortices have same
topological charge. For this case, partial solutions are found and a complete bifurcation analysis
is carried out. It is shown that, depending on the parameters of the Bose – Einstein condensate,
there are three different types of bifurcation diagrams. For each type, typical phase portraits
are presented.

Artemova E. M., Vetchanin E. V.
The Motion of an Unbalanced Circular Disk in the Field of a Point Source
2022, vol. 27, no. 1, pp. 2442
Abstract
Describing the phenomena of the surrounding world is an interesting task that
has long attracted the attention of scientists. However, even in seemingly simple phenomena,
complex dynamics can be revealed. In particular, leaves on the surface of various bodies of
water exhibit complex behavior. This paper addresses an idealized description of the mentioned
phenomenon. Namely, the problem of the planeparallel motion of an unbalanced circular disk
moving in a stream of simple structure created by a point source (sink) is considered. Note
that using point sources, it is possible to approximately simulate the work of skimmers used
for cleaning swimming pools. Equations of coupled motion of the unbalanced circular disk
and the point source are derived. It is shown that in the case of a fixedposition source of
constant intensity the equations of motion of the disk are Hamiltonian. In addition, in the case
of a balanced circular disk the equations of motion are integrable. A bifurcation analysis of
the integrable case is carried out. Using a scattering map, it is shown that the equations of
motion of the unbalanced disk are nonintegrable. The nonintegrability found here can explain
the complex motion of leaves in surface streams of bodies of water.

Artemova E. M., Karavaev Y. L., Mamaev I. S., Vetchanin E. V.
Dynamics of a Spherical Robot with Variable Moments of Inertia and a Displaced Center of Mass
2020, vol. 25, no. 6, pp. 689706
Abstract
The motion of a spherical robot with periodically changing moments of inertia,
internal rotors and a displaced center of mass is considered. It is shown that, under some
restrictions on the displacement of the center of mass, the system of interest features chaotic
dynamics due to separatrix splitting. A stability analysis is made of the upper equilibrium
point of the ball and of the periodic solution arising in its neighborhood, in the case of periodic
rotation of the rotors. It is shown that the lower equilibrium point can become unstable in the
case of fixed rotors and periodically changing moments of inertia.

Kilin A. A., Artemova E. M.
Integrability and Chaos in Vortex Lattice Dynamics
2019, vol. 24, no. 1, pp. 101113
Abstract
This paper is concerned with the problem of the interaction of vortex lattices, which
is equivalent to the problem of the motion of point vortices on a torus. It is shown that the
dynamics of a system of two vortices does not depend qualitatively on their strengths. Steadystate
configurations are found and their stability is investigated. For two vortex lattices it is
also shown that, in absolute space, vortices move along closed trajectories except for the case
of a vortex pair. The problems of the motion of three and four vortex lattices with nonzero
total strength are considered. For three vortices, a reduction to the level set of first integrals
is performed. The nonintegrability of this problem is numerically shown. It is demonstrated
that the equations of motion of four vortices on a torus admit an invariant manifold which
corresponds to centrally symmetric vortex configurations. Equations of motion of four vortices
on this invariant manifold and on a fixed level set of first integrals are obtained and their
nonintegrability is numerically proved.
