Geodesic
On a chain on cone problem
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 17 (2017) no. 4, pp. 57-63

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We consider a loop of a chain thrown like a lasso on a fixed right circular cone. The system is in the standard homogeneous gravity field. The axis of the cone is vertical. It is shown that under certain vertex angles chain's loop has an oblique equilibrium.
Keywords: variational methods, equilibriums of chains. 
O. E. Zubelevich. On a chain on cone problem. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 17 (2017) no. 4, pp. 57-63. http://geodesic.mathdoc.fr/item/VNGU_2017_17_4_a5/
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[1] A. P. Yushkevich (ed.), History of Mathematics from Ancient Times to the Beginning of 19 Century, v. 2, Nauka, M., 1970 (in Russian)

[2] L. S. Polak, William Hamilton, Nauka, M., 1993 (in Russian)