Geodesic
The Hess--Appelrot system and its nonholonomic analogs
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems of mathematics, mechanics, and mathematical physics. II, Tome 294 (2016), pp. 268-292

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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 the phase space) is discussed. 
@article{TM_2016_294_a16,
     author = {I. A. Bizyaev and A. V. Borisov and I. S. Mamaev},
     title = {The {Hess--Appelrot} system and its nonholonomic analogs},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {268--292},
     publisher = {mathdoc},
     volume = {294},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2016_294_a16/}
}
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I. A. Bizyaev; A. V. Borisov; I. S. Mamaev. The Hess--Appelrot system and its nonholonomic analogs. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems of mathematics, mechanics, and mathematical physics. II, Tome 294 (2016), pp. 268-292. http://geodesic.mathdoc.fr/item/TM_2016_294_a16/