The action-angle variables in theory of superconductivity and superfluidity

The problem on two bodies, interacting in such a way that they perform rotary motion in the euclidean (pseudo-euclidean) space is considered within the frames of the classical mechanics formalism. It is shown on the basis of the Hamiltonian motion equations that the system under consideration may be described in the action-angle variables. Its phase space in spite of its flatness is characterized by the Keller diversity, which makes it possible to perform exact quantization of the classic system. Results of quantization are easily identified with all already known models, describing the events of superconductivity and superfluidity