The Goryachov–Chaplygin top and the inverse scattering method

It is shown that the Goryachov–Chaplygin top can be treated within the framework of the inverse scattering method. A new method based on the $R$-matrix formalism is proposed to derive the equations determining the spectrum of the quantum integrals of motion. The method is of rather general nature and could present an alternative to the so called algebraic Bethe ansatz method.