On the Cases of Kirchhoff and Chaplygin of the Kirchhoff Equations
  It is proven that the general Kirchhoff case of the Kirchhoff equations for $B\ne 0$ is not algebraic complete integrable system. Similar analytic behavior of the general solution of the Chaplygin case is detected. Four-dimensional analogues of the Kirchhoff and the Chaplygin cases are defined on $e(4)$ with the standard Lie-Poisson bracket. 
Vladimir Dragovic, Borislav Gajic
math-ph math.MP nlin.SI