Geometrisation of Chaplygin's reducing multiplier theorem
  We develop the reducing multiplier theory for a special class of nonholonomic dynamical systems and show that the non-linear Poisson brackets naturally obtained in the framework of this approach are all isomorphic to the Lie-Poisson $e(3)$-bracket. As two model examples, we consider the Chaplygin ball problem on the plane and the Veselova system. In particular, we obtain an integrable gyrostatic generalisation of the Veselova system. 
Alexey V. Bolsinov, Alexey V. Borisov and Ivan S. Mamaev
math.DS