Geodesic
New integral in nonholonomic Painlev{\'e}--Chaplygin problem
Russian journal of nonlinear dynamics, Tome 2 (2006) no. 2, pp. 193-198.

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In the paper we present a new integral of motion in the problem of rolling motion of a heavy symmetric sphere on the surface of a paraboloid. We use this integral to study the Lyapunov stability of some trivial steady rotations.
Keywords: dynamical system, non-holonomic constraint, integral, periodic solution, Lyapunov stability. 
@article{ND_2006_2_2_a3,
     author = {A. A. Kilin},
     title = {New integral in nonholonomic {Painlev{\'e}--Chaplygin} problem},
     journal = {Russian journal of nonlinear dynamics},
     pages = {193--198},
     publisher = {mathdoc},
     volume = {2},
     number = {2},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ND_2006_2_2_a3/}
}
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A. A. Kilin. New integral in nonholonomic Painlev{\'e}--Chaplygin problem. Russian journal of nonlinear dynamics, Tome 2 (2006) no. 2, pp. 193-198. http://geodesic.mathdoc.fr/item/ND_2006_2_2_a3/