Geodesic
First Integrals of Groups of Complex Linear Transformations and of Natural Mechanical Systems with Homogeneous Potential
Matematičeskie zametki, Tome 70 (2001) no. 6, pp. 839-844

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We study the existence problem for rational first integrals of groups of complex linear transformations. The results obtained are used to study natural mechanical systems with homogeneous potential, in particular, the Suslov problem of motion of a rigid body about a fixed point under a nonholonomic constraint in the Kozlov case of zero constant energy. 
@article{MZM_2001_70_6_a2,
     author = {S. L. Ziglin},
     title = {First {Integrals} of {Groups} of {Complex} {Linear} {Transformations} and of {Natural} {Mechanical} {Systems} with {Homogeneous} {Potential}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {839--844},
     publisher = {mathdoc},
     volume = {70},
     number = {6},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2001_70_6_a2/}
}
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S. L. Ziglin. First Integrals of Groups of Complex Linear Transformations and of Natural Mechanical Systems with Homogeneous Potential. Matematičeskie zametki, Tome 70 (2001) no. 6, pp. 839-844. http://geodesic.mathdoc.fr/item/MZM_2001_70_6_a2/