Publications

2025

• 1.

  Artemova E. M., Lagunov D. A.

  The motion of a balanced circular foil in the field of fixed point sources
  Bulletin of Udmurt University. Mathematics. Mechanics. Computer Science, 2025, vol. 35, no. 4, pp. 601-618

  Abstract          pdf  (1.49 Mb)

  This paper is concerned with the motion of a circular foil in an ideal incompressible fluid containing two fixed point sources. It is shown that the study of such a system reduces to investigating the motion of a material point (the geometric center of the foil) in a potential field. Fixed points of the system corresponding to stationary configurations of the foil in absolute space are found. An analysis is made of the limiting case with sources whose intensities are opposite in sign, but have the same absolute value and which are contracted to a single point, that is, the motion of the foil in the field of a fixed dipole is considered. It is shown that in this case the system is integrable, and a complete analysis of the system is carried out.

  
  

  Keywords:	ideal fluid, circular foil, point source, Hamiltonian form
  Citation:	Artemova E. M., Lagunov D. A., The motion of a balanced circular foil in the field of fixed point sources , Bulletin of Udmurt University. Mathematics. Mechanics. Computer Science, 2025, vol. 35, no. 4, pp. 601-618
  DOI:	10.35634/vm250406
  Full text:	pdf (1.49 Mb)

  Journal Info

  Impact-factor WoS (2022):	0.500
  Impact-factor RSCI (2022):	0.342 (Q3)
  ISSN (print):	1994-9197
  ISSN (online):	2076-5959
  Site:	http://vst.ics.org.ru
• 2.

  Vetchanin E. V., Mamaev I. S., Lagunov D. A.

  Motion of Point Vortices and a Smooth Foil with Variable Mass Distribution in an Ideal Fluid
  Russian Journal of Nonlinear Dynamics, 2025, vol. 21, no. 4, pp. 515-537

  Abstract          pdf  (1.18 Mb)

  This paper considers the motion of an elliptic foil in the presence of point vortices. For the case of a vortex pair, a bifurcation analysis of the relative equilibria (a generalization of Föppl solutions) is carried out. These solutions correspond to the motion of the system on an invariant manifold on which the dynamics is governed by a system with $\frac{3}{2}$ degrees of freedom. Using a period advance Poincaré map, a numerical analysis of the dynamics on the invariant manifold is performed for the case where the center of mass of the system moves periodically in an impulse-like manner. The occurrence of new periodic, quasiperiodic and chaotic modes of motion is demonstrated.

  
  

  Keywords:	Föppl solutions, point vortices, bifurcation analysis, parametric excitation
  Citation:	Vetchanin E. V., Mamaev I. S., Lagunov D. A., Motion of Point Vortices and a Smooth Foil with Variable Mass Distribution in an Ideal Fluid, Russian Journal of Nonlinear Dynamics, 2025, vol. 21, no. 4, pp. 515-537
  DOI:	10.20537/nd251207
  Full text:	pdf (1.18 Mb)

  Journal Info

  Impact-factor RSCI (2022):	0.259 (Q3)
  ISSN (print):	2658-5324
  ISSN (online):	2658-5316
  Site:	http://nd.ics.org.ru/
• 3.

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

  The Motion of an Elliptic Foil in the Field of a Fixed Vortex Source
  Russian Journal of Nonlinear Dynamics, 2025, vol. 21, no. 2, pp. 135-155

  Abstract          pdf  (660.51 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, Russian Journal of Nonlinear Dynamics, 2025, vol. 21, no. 2, pp. 135-155
  DOI:	10.20537/nd241203
  Full text:	pdf (660.51 Kb)

  Journal Info

  Impact-factor RSCI (2022):	0.259 (Q3)
  ISSN (print):	2658-5324
  ISSN (online):	2658-5316
  Site:	http://nd.ics.org.ru/