The problem of the stability of circular rings connected to each other

The paper considers the problems on the stability of a system of circular rings interconnected in such a way that the displacements of these rings and the rotation angles of their sections coincide at some points. This problem is reduced to some variational problem with restrictions on the desired functions in the form of linear equations. The Fourier series are used for a finite-dimensional approximation. The paper also presents the problem on the stability of a system of circular rings reinforced with inextensible threads that do not withstand compressive forces. In this case, there are constraints in the form of inequalities, and after a finite-dimensional approximation, the problem is reduced to finding bifurcation points for nonlinear programming problems in the presence of constraints in the form of inequalities.