Geodesic
Demchenko's nonholonomic case of a gyroscopic ball rolling without sliding over a sphere after his 1923 Belgrade doctoral thesis
Theoretical and applied mechanics, Tome 47 (2020) no. 2, p. 257

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We present an integrable nonholonomic case of rolling without sliding of a gyroscopic ball over a sphere. This case was introduced and studied in detail by Vasilije Demchenko in his 1923 doctoral dissertation defended at the University of Belgrade, with Anton Bilimović as the advisor. These results are absolutely unknown to modern researchers. The study is based on the C. Neumann coordinates and the Voronec principle. By using the involved technique of elliptic functions, a detailed study of motion is performed. Several special classes of trajectories are distinguished, including regular and pseudo-regular precessions. The so-called remarkable trajectories, introduced by Paul Painlevé and Anton Bilimović, are described in the present case. The historical context of the results as well as their place in contemporary mechanics are outlined.
DOI : 10.2298/TAM201106015D
Classification : 37J60, 01A60, 33E05, 01A72, 70F25, 53Z05
Keywords: nonholonimic dynamics, rolling without sliding, C. Neumann coordinates, elliptic functions, elliptic integrals, Voronec principle, regular and pseudo-regular precessions, remarkable trajectories 
Vladimir Dragović; Borislav Gajić; Božidar Jovanović. Demchenko's nonholonomic case of a gyroscopic ball rolling without sliding over a sphere after his 1923 Belgrade doctoral thesis. Theoretical and applied mechanics, Tome 47 (2020) no. 2, p. 257 . doi: 10.2298/TAM201106015D
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     title = {Demchenko's nonholonomic case of a gyroscopic ball rolling without sliding over a sphere after his 1923 {Belgrade} doctoral thesis},
     journal = {Theoretical and applied mechanics},
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