New integrable problem of classical mechanics
The main result is that the rotation of an arbitrary rigid body with a fixed point in a Newtonian field given by an arbitrary quadratic potential is completely integrable in the sense of Liouville's integrability theorem. The dynamical equations are integrated explicitely in terms of the Riemann \(\theta\)-functions of four variables, restricted to a three-dimensional manifold (a Prym variety). As a consequence of this the rotation of a rigid body fixed at its center of mass under the action of a Newtonian field of a remote gravitating object is completely integrable in the second order approximation.
scientific article; zbMATH DE number 3922030