New integrable cases in the dynamics of rigid bodies
The problem of motion of a rigid body about a fixed point under the action of conservative potential and gyroscopic forces was treated in great detail only in the case when these forces admit a common axis of symmetry passing through the fixed point. In this version of the problem, six general integrable cases are known. In addition, over twenty particular solutions are also known. In spite of its practical importance, the case of non-axial symmetry has escaped attention for a long time. There are only one general and one particular known integrable cases. In the present paper we introduce four new general integrable cases three of which deal with problems having no axial symmetry.
scientific article; zbMATH DE number 3980557