Tatyana Ivanova

    Tatyana Ivanova
    1, Universitetskaya str., Izhevsk, 426034, Russia
    Udmurt State University

    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.


    Kilin A. A., Ivanova T. B.
    This paper addresses the problem of a sphere with axisymmetric mass distribution rolling on a horizontal plane. It is assumed that there is no slipping of the sphere as it rolls in the direction of the projection of the symmetry axis onto the supporting plane. It is also assumed that, in the direction perpendicular to the above-mentioned one, the sphere can slip relative to the plane. Examples of realization of the above-mentioned nonholonomic constraint are given. Equations of motion are obtained and their first integrals are found. It is shown that the system under consideration admits a redundant set of first integrals, which makes it possible to perform reduction to a system with one degree of freedom.
    Keywords: nonholonomic constraint, first integral, integrability, reduction
    Citation: Kilin A. A., Ivanova T. B.,  The Integrable Problem of the Rolling Motion of a Dynamically Symmetric Spherical Top with One Nonholonomic Constraint, Rus. J. Nonlin. Dyn., 2023, Vol. 19, no. 1, pp.  3-17
    Ivanova T. B.
    This paper is concerned with the rolling of a homogeneous ball with slipping on a uniformly rotating horizontal plane. We take into account viscous friction forces arising when there is slipping at the contact point. It is shown that, as the coefficient of viscosity tends to infinity, the solution of the generalized problem on each fixed time interval tends to a solution of the corresponding nonholonomic problem.
    Keywords: rotating surface, turntable, nonholonomic constraint, rolling ball, sliding, viscous friction
    Citation: Ivanova T. B.,  The Rolling of a Homogeneous Ball with Slipping on a Horizontal Rotating Plane, Rus. J. Nonlin. Dyn., 2019, Vol. 15, no. 2, pp.  171-178
    Borisov A. V., Karavaev Y. L., Mamaev I. S., Erdakova N. N., Ivanova T. B., Tarasov V. V.
    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 high-speed 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 well-known experimental and theoretical results in this area.
    Keywords: dry friction, linear pressure distribution, two-dimensional motion, planar motion, Coulomb law
    Citation: Borisov A. V., Karavaev Y. L., Mamaev I. S., Erdakova N. N., Ivanova T. B., Tarasov V. V.,  On the dynamics of a body with an axisymmetric base sliding on a rough plane, Rus. J. Nonlin. Dyn., 2015, Vol. 11, No. 3, pp.  547-577
    Borisov A. V., Erdakova N. N., Ivanova T. B., Mamaev I. S.
    In this paper we investigate the dynamics of a body with a flat base sliding on a inclined plane under the assumption of linear pressure distribution of the body on the plane as the simplest dynamically consistent friction model. Computer-aided analysis of the system’s dynamics on the inclined plane using phase portraits has allowed us to reveal dynamical effects that have not been found earlier.
    Keywords: dry friction, linear pressure distribution, two-dimensional motion, planar motion, Coulomb law
    Citation: Borisov A. V., Erdakova N. N., Ivanova T. B., Mamaev I. S.,  On the dynamics of a body with an axisymmetric base sliding on a rough plane, Rus. J. Nonlin. Dyn., 2014, Vol. 10, No. 4, pp.  483-495
    Ivanova T. B., Pivovarova E. N.
    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.
    Keywords: control, dry friction, Chaplygin’s ball, spherical robot
    Citation: Ivanova T. B., Pivovarova E. N.,  Comment on the paper by A.V. Borisov, A.A. Kilin, I.S. Mamaev “How to control the Chaplygin ball using rotors. II”, Rus. J. Nonlin. Dyn., 2014, Vol. 10, No. 1, pp.  127-131
    Ivanova T. B., Pivovarova E. N.
    This paper investigates the possibility of the motion control of a ball with a pendulum mechanism with non-holonomic constraints using gaits — the simplest motions such as acceleration and deceleration during the motion in a straight line, rotation through a given angle and their combination. Also, the controlled motion of the system along a straight line with a constant acceleration is considered. For this problem the algorithm for calculating the control torques is given and it is shown that the resulting reduced system has the first integral of motion.
    Keywords: non-holonomic constraint, control, spherical shell, integral of motion
    Citation: Ivanova T. B., Pivovarova E. N.,  Dynamics and Control of a Spherical Robot with an Axisymmetric Pendulum Actuator, Rus. J. Nonlin. Dyn., 2013, Vol. 9, No. 3, pp.  507-520
    Mamaev I. S., Ivanova T. B.
    In this paper we consider the dynamics of rigid body whose sharp edge is in contact with a rough plane. The body can move so that its contact point does not move or slips or loses touch with the support. In this paper, the dynamics of the system is considered within three mechanical models that describe different modes of motion. The boundaries of definition range of each model are given, the possibility of transitions from one mode to another and their consistency with different coefficients of friction on the horizontal and inclined surfaces is discussed.
    Keywords: rod, Painlevé paradox, dry friction, separation, frictional impact
    Citation: Mamaev I. S., Ivanova T. B.,  The dynamics of rigid body whose sharp edge is in contact with a inclined surface with dry friction, Rus. J. Nonlin. Dyn., 2013, Vol. 9, No. 3, pp.  567-594
    Treschev D. V., Erdakova N. N., Ivanova T. B.
    The problem of a uniform straight cylinder (disc) sliding on a horizontal plane under the action of dry friction forces is considered. The contact patch between the cylinder and the plane coincides with the base of the cylinder. We consider axisymmetric discs, i.e. we assume that the base of the cylinder is symmetric with respect to the axis lying in the plane of the base. The focus is on the qualitative properties of the dynamics of discs whose circular base, triangular base and three points are in contact with a rough plane.
    Keywords: Amontons–Coulomb law, dry friction, disc, final dynamics, stability
    Citation: Treschev D. V., Erdakova N. N., Ivanova T. B.,  On the final motion of cylindrical solids on a rough plane, Rus. J. Nonlin. Dyn., 2012, Vol. 8, No. 3, pp.  585-603
    Kuleshov A. S., Treschev D. V., Ivanova T. B., Naymushina O. S.
    A rigid cylinder on a viscoelastic plane
    2011, Vol. 7, No. 3, pp.  601-625
    The paper considers two two-dimensional dynamical problems for an absolutely rigid cylinder interacting with a deformable flat base (the motion of an absolutely rigid disk on a base which in non-deformed condition is a straight line). The base is a sufficiently stiff viscoelastic medium that creates a normal pressure $p(x) = kY(x)+ν\dot{Y}(x)$, where $x$ is a coordinate on the straight line, $Y(x)$ is a normal displacement of the point $x$, and $k$ and $ν$ are elasticity and viscosity coefficients (the Kelvin—Voigt medium). We are also of the opinion that during deformation the base generates friction forces, which are subject to Coulomb’s law. We consider the phenomenon of impact that arises during an arbitrary fall of the disk onto the straight line and investigate the disk’s motion «along the straight line» including the stages of sliding and rolling.
    Keywords: Kelvin–Voight medium, impact, viscoelasticity, friction
    Citation: Kuleshov A. S., Treschev D. V., Ivanova T. B., Naymushina O. S.,  A rigid cylinder on a viscoelastic plane, Rus. J. Nonlin. Dyn., 2011, Vol. 7, No. 3, pp.  601-625
    Borisov A. V., Mamaev I. S., Ivanova T. B.
    We consider figures of equilibrium and stability of a liquid self-gravitating elliptic cylinder. The flow within the cylinder is assumed to be dew to an elliptic perturbation. A bifurcation diagram is plotted and conditions for steady solutions to exist are indicated.
    Keywords: self-gravitating liquid, elliptic cylinder, bifurcation point, stability, Riemann equations
    Citation: Borisov A. V., Mamaev I. S., Ivanova T. B.,  Stability of a liquid self-gravitating elliptic cylinder with intrinsic rotation, Rus. J. Nonlin. Dyn., 2010, Vol. 6, No. 4, pp.  807-822

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