Geodesic
Generalizations of the Kovalevskaya case and quaternions
Informatics and Automation, Modern problems of mechanics, Tome 295 (2016), pp. 41-52

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This paper provides a detailed description of various reduction schemes in rigid body dynamics. The analysis of one of such nontrivial reductions makes it possible to put the cases already found in order and to obtain new generalizations of the Kovalevskaya case to $e(3)$. Note that the indicated reduction allows one to obtain in a natural way some singular additive terms that were proposed earlier by D. N. Goryachev. 
@article{TRSPY_2016_295_a2,
     author = {I. A. Bizyaev and A. V. Borisov and I. S. Mamaev},
     title = {Generalizations of the {Kovalevskaya} case and quaternions},
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     volume = {295},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2016_295_a2/}
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I. A. Bizyaev; A. V. Borisov; I. S. Mamaev. Generalizations of the Kovalevskaya case and quaternions. Informatics and Automation, Modern problems of mechanics, Tome 295 (2016), pp. 41-52. http://geodesic.mathdoc.fr/item/TRSPY_2016_295_a2/