Publications

Online First Articles

• 1.

  Bizyaev I. A., Vetchanin E. V.

  Climb of the Chaplygin Sleigh on an Inclined Plane under Periodic Controls: Speedup and Uniform Motion
  Rus. J. Nonlin. Dyn., 2024

  Abstract          pdf  (613.1 Kb)

  This paper addresses the problem of the Chaplygin sleigh moving on an inclined plane under the action of periodic controls. Periodic controls are implemented by moving point masses. It is shown that, under periodic oscillations of one point mass in the direction perpendicular to that of the knife edge, for a nonzero initial velocity there exists a motion with acceleration or a uniform motion (on average per period) in the direction opposite to that of the largest descent. It is shown that adding to the system two point masses which move periodically along some circle enables a period-averaged uniform motion of the system from rest.

  
  

  Keywords:	Chaplygin sleigh, motion on an inclined plane, speedup, nonholonomic mechanics
  Citation:	Bizyaev I. A., Vetchanin E. V., Climb of the Chaplygin Sleigh on an Inclined Plane under Periodic Controls: Speedup and Uniform Motion, Rus. J. Nonlin. Dyn., 2024, https://doi.org/10.20537/nd241202
  DOI:	10.20537/nd241202
  Full text:	pdf  (613.1 Kb)
• 2.

  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)