On nonlinear stability of the regular vortex systems on a sphere.

Energy-Momentum Stability of Icosahedral Configurations of Point Vortices on a Sphere

Invariant Dynamical Systems in the N-vortex Problem on the Sphere and Unstable Motion of the N-ring

We consider the system of the N vortex points with the identical strength on a sphere. As a local effect of the rotation of the sphere, we fix vortex points at the both poles, which are called the pole vortices. When the N vortex points are equally spaced along the line of latitude of the sphere, the configuration is called the “N -ring” or “N -gon”. It is a relative fixed configuration[3,4] an...

Stability of Thomson’s Configurations of Vortices Ona Sphere

In this work stability of polygonal configurations on a plane and sphere is investigated. The conditions of linear stability are obtained. A nonlinear analysis of the problem is made with the help of Birkhoff normalization. Some problems are also formulated. 1 A linear stability of Thomson’s configurations of vortices on a sphere Motion equations of a system of N point vortices on a sphere can ...

Numerical Investigation of Vortex Interaction in Pipe Flow

To discover the nonlinear characteristics of pipe flow, we simulated the flow as a sum of many vortex rings. As a first step, we investigated the nonlinear interaction among a maximum of three vortex rings. The pipe wall was replaced by many bound vortices. A free vortex ring moves right or left according to the radius, and that of a particular radius keeps the initial position. The energy of a...

A new approach based on state conversion to stability analysis and control design of switched nonlinear cascade systems

In this paper, the problems of control and stabilization of switched nonlinear cascade systems is investigated. The so called simultaneous domination limitation (SDL) is introduced in previous works to assure the existence of a common quadratic Lyapunov function (CQLF) for switched nonlinear cascade systems. According to this idea, if all subsystems of a switched system satisfy the SDL, a CQLF ...