Publications

Online First Articles

• 1.

  Artemova E. M., Lagunov D. A., Vetchanin E. V.

  The Motion of an Elliptic Foil in the Field of a Fixed Vortex Source
  Rus. J. Nonlin. Dyn., 2024

  Abstract          pdf  (656.91 Kb)

  This paper is concerned with the motion of an elliptic foil in the field of a fixed point singularity. A complex potential of the fluid flow is constructed, and the forces and the torque which act on the foil from the fluid are obtained. It is shown that the equations of motion of the elliptic foil in the field of a fixed point vortex source can be represented as Lagrange – Euler equations. It is also shown that the system has an additional first integral due to the conservation of the angular momentum. An effective potential of the system under consideration is constructed. For the cases where the singularity is a vortex or a source, unstable relative equilibrium points corresponding to the circular motion of the foil around the singularity are found.

  
  

  Keywords:	ideal fluid, elliptic foil, point vortex, point source, Lagrangian form, Hamiltonian form
  Citation:	Artemova E. M., Lagunov D. A., Vetchanin E. V., The Motion of an Elliptic Foil in the Field of a Fixed Vortex Source, Rus. J. Nonlin. Dyn., 2024, https://doi.org/10.20537/nd241203
  DOI:	10.20537/nd241203
  Full text:	pdf  (656.91 Kb)
• 2.

  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)
• 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)