Generalized Kowalevski top: new integrable cases on $e(3)$ and $so(4)$

Abstract

A three-parameter family of integrable quadratic Hamiltonians on $e(3)$ and $so(4)$ is presented. When one of the parameters vanishes, the Hamiltonian coincides with the Kowalevski Hamiltonian with the girostatic term. If the other two parameters are equal to zero then the Hamiltonian reduces to a new integrable case of the Kirchhoff equations found recently by the author.