Tatyana Ivanova
In 2004 graduated from Udmurt State University (UdSU), Izhevsk, Russia.
since 2004: lecturer of Department of Theoretical Physics at UdSU.
since 2010: scientist of Department of Vortex Dynamics of Laboratory of Nonlinear Analysis and the Design of New Types of Vehicles at UdSU.
2012: Thesis of Ph.D. (candidate of science). Thesis title: «Numerical and analytical studies of stationary and bifurcation processes in the systems of hydrodynamical type», Moscow Engineering Physics Institute.
Publications:
Kilin A. A., Ivanova T. B., Pivovarova E. N.
Stabilization of Steady Rotations of a Spherical Robot on a Vibrating Base Using Feedback
2023, vol. 28, no. 6, pp. 888905
Abstract
This paper treats the problem of a spherical robot with an axisymmetric pendulum
drive rolling without slipping on a vibrating plane. The main purpose of the paper is to
investigate the stabilization of the upper vertical rotations of the pendulum using feedback
(additional control action). For the chosen type of feedback, regions of asymptotic stability
of the upper vertical rotations of the pendulum are constructed and possible bifurcations are
analyzed. Special attention is also given to the question of the stability of periodic solutions
arising as the vertical rotations lose stability.

Kilin A. A., Pivovarova E. N., Ivanova T. B.
Spherical Robot of Combined Type: Dynamics and Control
2015, vol. 20, no. 6, pp. 716728
Abstract
This paper is concerned with free and controlled motions of a spherical robot of combined type moving by displacing the center of mass and by changing the internal gyrostatic momentum. Equations of motion for the nonholonomic model are obtained and their first integrals are found. Fixed points of the reduced system are found in the absence of control actions. It is shown that they correspond to the motion of the spherical robot in a straight line and in a circle. A control algorithm for the motion of the spherical robot along an arbitrary trajectory is presented. A set of elementary maneuvers (gaits) is obtained which allow one to transfer the spherical robot from any initial point to any end point.

Borisov A. V., Karavaev Y. L., Mamaev I. S., Erdakova N. N., Ivanova T. B., Tarasov V. V.
Experimental Investigation of the Motion of a Body with an Axisymmetric Base Sliding on a Rough Plane
2015, vol. 20, no. 5, pp. 518541
Abstract
In this paper we investigate the dynamics of a body with a flat base (cylinder) sliding on a horizontal rough plane. For analysis we use two approaches. In one of the approaches using a friction machine we determine the dependence of friction force on the velocity of motion of cylinders. In the other approach using a highspeed camera for video filming and the method of presentation of trajectories on a phase plane for analysis of results, we investigate the qualitative and quantitative behavior of the motion of cylinders on a horizontal plane. We compare the results obtained with theoretical and experimental results found earlier. In addition, we give a systematic review of the wellknown experimental and theoretical results in this area.

Borisov A. V., Erdakova N. N., Ivanova T. B., Mamaev I. S.
The Dynamics of a Body with an Axisymmetric Base Sliding on a Rough Plane
2014, vol. 19, no. 6, pp. 607634
Abstract
In this paper we investigate the dynamics of a body with a flat base sliding on a horizontal and inclined rough plane under the assumption of linear pressure distribution of the body on the plane as the simplest dynamically consistent friction model. For analysis we use the descriptive function method similar to the methods used in the problems of Hamiltonian dynamics with one degree of freedom and allowing a qualitative analysis of the system to be made without explicit integration of equations of motion. In addition, we give a systematic review of the wellknown experimental and theoretical results in this area.

Mamaev I. S., Ivanova T. B.
The Dynamics of a Rigid Body with a Sharp Edge in Contact with an Inclined Surface in the Presence of Dry Friction
2014, vol. 19, no. 1, pp. 116139
Abstract
In this paper we consider the dynamics of a rigid body with a sharp edge in contact with a rough plane. The body can move so that its contact point is fixed or slips or loses contact with the support. In this paper, the dynamics of the system is considered within three mechanical models which describe different regimes of motion. The boundaries of the domain of definition of each model are given, the possibility of transitions from one regime to another and their consistency with different coefficients of friction on the horizontal and inclined surfaces are discussed.

Ivanova T. B., Pivovarova E. N.
Comments on the Paper by A.V. Borisov, A.A. Kilin, I.S. Mamaev "How to Control the Chaplygin Ball Using Rotors. II"
2014, vol. 19, no. 1, pp. 140143
Abstract
In this paper we consider the control of a dynamically asymmetric balanced ball on a plane in the case of slipping at the contact point. Necessary conditions under which a control is possible are obtained. Specific algorithms of control along a given trajectory are constructed.
