The stability problem of a moving circular cylinder
of radius R and a system of n identical point vortices uniformly distributed on a circle of radius R0 is considered. The circulation around the cylinder is zero. There are three parameters in the problem: the number of point vortices n, the added mass of the cylinder a and parameter q = R²/ R²₀.
The linearization matrix and the quadratic part of the Hamiltonian of the problem are studied. As a result, the parameter space of the problem is divided into the area of linear stability, where nonlinear analysis is required, and the instability area. In the case n = 2, 3 two domains of linear stability are found. In the case n = 4, 5, 6 there is found one domain. In the case n > 7, the studied solution is unstable for all of problem parameters values. The obtained results in the limiting case at a → ∞ agree with the known results for the model of point vortices outside the circular domain.