On the analytic non-integrability of the Rattleback problem
  We establish the analytic non-integrability of the nonholonomic ellipsoidal rattleback model for a large class of parameter values. Our approach is based on the study of the monodromy group of the normal variational equations around a particular orbit. The embedding of the equations of the heavy rigid body into the rattleback model is discussed. 
Holger R. Dullin and Alexei Tsygvintsev