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Section
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Mechanics
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Title
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Stability analysis of periodic solutions in the problem of the rolling of a ball with a pendulum
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Author(-s)
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Pivovarova E.N.a,
Ivanova T.B.a
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Affiliations
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Udmurt State Universitya
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Abstract
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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.
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Keywords
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rolling motion, stability, Lagrange’s gyroscope, bifurcational diagram
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UDC
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531.31
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MSC
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37J60
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DOI
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10.20537/vm120412
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Received
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13 August 2012
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Language
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Russian
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Citation
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Pivovarova E.N., Ivanova T.B. Stability analysis of periodic solutions in the problem of the rolling of a ball with a pendulum, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2012, issue 4, pp. 146-155.
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References
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Full text
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