The Hess-Appelrot system and its nonholonomic analogs
  This paper is concerned with the nonholonomic Suslov problem and its generalization proposed by Chaplygin. The issue of the existence of an invariant measure with singular density (having singularities at some points of phase space) is discussed. 
Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev
nlin.SI