Geodesic
Stability analysis of periodic solutions in the problem of the rolling of a~ball with a~pendulum
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 4 (2012), pp. 146-155

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In the paper we study the stability of a spherical shell rolling on a horizontal plane with Lagrange's gyroscope inside. A linear stability analysis is made for the upper and lower position of a top. A bifurcation diagram of the system is constructed. The trajectories of the contact point for different values of the integrals of motion are constructed and analyzed.
Keywords: rolling motion, stability, Lagrange’s gyroscope, bifurcational diagram. 
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     author = {E. N. Pivovarova and T. B. Ivanova},
     title = {Stability analysis of periodic solutions in the problem of the rolling of a~ball with a~pendulum},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {146--155},
     publisher = {mathdoc},
     number = {4},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2012_4_a11/}
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E. N. Pivovarova; T. B. Ivanova. Stability analysis of periodic solutions in the problem of the rolling of a~ball with a~pendulum. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 4 (2012), pp. 146-155. http://geodesic.mathdoc.fr/item/VUU_2012_4_a11/