References
A. V. Borisov and Yu. N. Fedorov, Vestn. Mosk. Univ., Ser. Mat. Mech., No. 6, 793 (1995).
A. V. Borisov and I. S. Mamaev, Reg. Chaot. Dyn. 7(2), 177 (2002).
L. P. Eisenhart, Ann. Math. 35(2), 284 (1934).
A. A. Kilin, Reg. Chaot. Dyn. 6(3), 291 (2001).
S. A. Chaplygin, To the Theory of Motion of Nonholonomic Systems. The Theorem of Reducing Factor, in Collected Works (OGIZ, Moscow, 1948), Vol. 1, pp. 15–25 [in Russian].
A. V. Borisov and I. S. Mamaev, Mat. Zametki 70, 793 (2001).
A. V. Borisov and I. S. Mamaev, Sib. Math. J. 48, 26 (2007) [Sib. Mat. Zh. 48 (1), 33 (2007)].
S. A. Chaplygin, On a Ball Rolling over a Horizontal Plane, in Collected Works (OGIZ, Moscow, 1948), Vol. 1, pp. 76–101 [in Russian].
A. V. Borisov and I. S. Mamaev, Dynamics of Solid Body (Moscow-Izhevsk, 2001) [in Russian].
V. V. Kozlov, Usp. Mekh. 8(3), 85 (1985).
A. P. Markeev, Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela 21(1), 65 (1986).
M. P. Kharlamov, Topological Analysis of the Classical Integrable Problems of Solid Body Dynamics (Leningrad. Gos. Univ., Leningrad, 1988) [in Russian].
V. G. Marikhin and V. V. Sokolov, Theor. Math. Phys. 149, 1425 (2006) [Teor. Mat. Fiz. 149 (2), 147 (2006)].
A. V. Borisov and I. S. Mamaev, Reg. Chaot. Dyn. 12(2), 153 (2007).
V. A. Yaroshchuk, Vestn. Mosk. Univ., Ser. Mat. Mech., No. 6, 26 (1992).
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Original Russian Text © A.V. Borisov, I.S. Mamaev, V.G. Marikhin, 2008, published in Doklady Akademii Nauk, 2008, Vol. 422, No. 4, pp. 475–478.
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Borisov, A.V., Mamaev, I.S. & Marikhin, V.G. Explicit integration of one problem in nonholonomic mechanics. Dokl. Phys. 53, 525–528 (2008). https://doi.org/10.1134/S1028335808100066
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DOI: https://doi.org/10.1134/S1028335808100066