Elizaveta Artemova

This paper addresses the problem of the motion of two point vortices of arbitrary strengths in an ideal incompressible fluid on a finite flat cylinder. A procedure of reduction to the level set of an additional first integral is presented. It is shown that, depending on the parameter values, three types of bifurcation diagrams are possible in the system. A complete bifurcation analysis of the system is carried out for each of them. Conditions for the orbital stability of generalizations of von Kármán streets for the problem under study are obtained.

This paper is concerned with the controlled motion of a three-link wheeled snake robot propelled by changing the angles between the central and lateral links. The limits on the applicability of the nonholonomic model for the problem of interest are revealed. It is shown that the system under consideration is completely controllable according to the Rashevsky – Chow theorem. Possible types of motion of the system under periodic snake-like controls are presented using Fourier expansions. The relation of the form of the trajectory in the space of controls to the type of motion involved is found. It is shown that, if the trajectory in the space of controls is centrally symmetric, the robot moves with nonzero constant average velocity in some direction.

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.