The Goryachev-Chaplygin top and the Toda lattice
The Goryachev-Chaplygin top is known to be a completely algebraically integrable system as a linear flow on a hyperelliptic Jacobian. In this paper it is proved that the invariant surfaces of the Goryachev-Chaplygin top are double covers of the Jacobian above ramified along the two translates of the theta divisor, touching in one point. The equations of motion for the Goryachev-Chaplygin top are shown to be an instance of a system of differential equations in 7 unknowns having 5 quadratic constants of motion which is related intimately with the system of equations for the 3-body periodic Toda lattice.
scientific article; zbMATH DE number 4040875