Abstract
With the aid of computer algebra methods, we have conducted qualitative analysis of the phase space for the classic and generalized Goryachev–Chaplygin problem. In particular, we have found a series of new invariant manifolds of various dimension which possess some extremal property. Motions on a one-dimensional invariant manifold have been investigated. It was shown that these motions are asymptotically stable on this manifold, and one of equilibrium points on the manifold is a limit point for these motions.
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Irtegov, V., Titorenko, T. (2014). Invariant Manifolds in the Classic and Generalized Goryachev–Chaplygin Problem. In: Gerdt, V.P., Koepf, W., Seiler, W.M., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2014. Lecture Notes in Computer Science, vol 8660. Springer, Cham. https://doi.org/10.1007/978-3-319-10515-4_16
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DOI: https://doi.org/10.1007/978-3-319-10515-4_16
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-10514-7
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