Publications

Online First Articles

• 1.

  Kilin A. A., Ivanova T. B., Karavaev Y. L., Yefremov K. S.

  Theoretical and experimental investigations of the controlled motion of a roller racer
  Theoretical and Applied Mechanics, 2024

  Abstract          pdf  (1.37 Mb)

  In this paper, we address the problem of the controlled motion of a roller racer on a plane. We assume that the angle between the platforms is a given periodic function of time (control function), and the no-slip conditions (nonholonomic constraint) and viscous friction forces act at the points of contact of the wheels with the plane. In this case, all trajectories of the reduced system tend asymptotically to a periodic solution. In this paper, we show that for a selected periodic control function there exists a motion of the system that is bounded (along a circle) and unbounded (along a straight line). Unbounded motion corresponds to the resonant case which takes place at zero average value of the control function. The theoretical dependence of the trajectory and the velocity of the roller racer on its parameters and the parameters of the selected control function is investigated. These dependences are confirmed experimentally.

  
  

  Citation	Kilin A. A., Ivanova T. B., Karavaev Y. L., Yefremov K. S., Theoretical and experimental investigations of the controlled motion of a roller racer, Theoretical and Applied Mechanics, 2024, https://doi.org/10.2298/TAM241203010K
  DOI:	10.2298/TAM241203010K
  Full text:	pdf  (1.37 Mb)
• 2.

  Kilin A. A., Karavaev Y. L.

  Experimental observation of stabilization of tippe top spinning on a vibrating plane
  Theoretical and Applied Mechanics, 2025

  Abstract          pdf  (840.04 Kb)

  
  

  Citation	Kilin A. A., Karavaev Y. L., Experimental observation of stabilization of tippe top spinning on a vibrating plane, Theoretical and Applied Mechanics, 2025, https://doi.org/10.2298/TAM241204001K
  DOI:	10.2298/TAM241204001K
  Full text:	pdf  (840.04 Kb)
• 3.

  Kilin A. A., Pivovarova E. N., Ivanova T. B.

  Rolling of a Homogeneous Ball on a Moving Cylinder
  Regular and Chaotic Dynamics, 2024

  Abstract          pdf  (710.83 Kb)

  This paper addresses the problem of a homogeneous ball rolling on the inner surface of a circular cylinder in a field of gravity parallel to its axis. It is assumed that the ball rolls without slipping on the surface of the cylinder, and that the cylinder executes plane-parallel motions in a circle perpendicular to its symmetry axis. The integrability of the problem by quadratures is proved. It is shown that in this problem the trajectories of the ball are quasiperiodic in the general case, and that an unbounded elevation of the ball is impossible. However, in contrast to a fixed (or rotating) cylinder, there exist resonances at which the ball moves on average downward with constant acceleration.

  
  

  Keywords:	homogeneous ball, nonholonomic constraint, surface of revolution, moving cylinder, unbounded drift, nonautonomous system, quadrature, integrability
  Citation:	Kilin A. A., Pivovarova E. N., Ivanova T. B., Rolling of a Homogeneous Ball on a Moving Cylinder, Regular and Chaotic Dynamics, 2024, https://doi.org/10.1134/S1560354724590027
  DOI:	10.1134/S1560354724590027
  Full text:	pdf  (710.83 Kb)
• 4.

  Kilin A. A., Gavrilova A. M., Artemova E. M.

  Dynamics of an Elliptic Foil with an Attached Vortex in an Ideal Fluid: The Integrable Case
  Regular and Chaotic Dynamics, 2024

  Abstract          pdf  (1.52 Mb)

  This paper is concerned with the plane-parallel motion of an elliptic foil with an attached vortex of constant strength in an ideal fluid. Special attention is given to the case in which the vortex lies on the continuation of one of the semiaxes of the ellipse. It is shown that in this case there exist no attracting solutions and the system is integrable by the Euler – Jacobi theorem. A complete qualitative analysis of the equations of motion is carried out for cases where the vortex lies on the continuation of the large or the small semiaxis of the ellipse. Possible types of trajectories of an elliptic foil with an attached vortex are established: quasi-periodic, unbounded (going to infinity) and periodic trajectories.

  
  

  Keywords:	ideal fluid, elliptic foil, point vortex, integrable system, bifurcation analysis
  Citation:	Kilin A. A., Gavrilova A. M., Artemova E. M., Dynamics of an Elliptic Foil with an Attached Vortex in an Ideal Fluid: The Integrable Case, Regular and Chaotic Dynamics, 2024, https://doi.org/10.1134/S1560354724590015
  DOI:	10.1134/S1560354724590015
  Full text:	pdf  (1.52 Mb)