Analytic non-integrability of the Suslov problem

In this work, we consider the Suslov problem, which consists of a rotation motion of a rigid body, whose center of mass is located at one axis of inertia, around a fixed point O in a constant gravity field restricted to a nonholonomic constraint. The integrability and non-integrability has been established by a number of authors for the nongeneric values of b = (b(1), b(2), b(3)) which is the unit vector along the line connecting the point O with the center of mass of the body. Here, we prove the analytic non-integrability for the remaining (generic) values of b. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4763464]