Abstract
Some problems of obtaining, analysis of stability and bifurcations of invariant sets of dynamical systems described by Euler equations in Lie algebras so(4) and so(3,1) are discussed. The considered systems assume additional polynomial first integrals of the 3rd and 6th degrees. Invariant sets of these systems can be found from the conditions of stationarity for the problem first integrals. Methods of computer algebra have been employed in the capacity of the computational methods. The computer algebra systems (CAS) Mathematica and Maple have been used.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Borisov, A.V., Mamayev, I.S., Sokolov, V.V.: A new integrable case on so (4). Dokl. Phys. 46(12), 888–889 (2001)
Sokolov, V.V.: A new integrable case for the Kirchhoff equation. Theoret. and Math. Phys. 129(1), 1335–1340 (2001)
Sokolov, V.V.: On a class of quadratic Hamiltonians on so (4). Dokl. Math. 69, 108–111 (2004)
Bogoyavlensky, O.I.: Breaking Solitons. Nonlinear Integrable Equations. Moscow, Nauka (1991)
Smirnov, A.V.: Systems of sl(2,c) tops as two-particle systems. Theoret. and Math. Phys. 157(1), 1370–1382 (2008)
Tsiganov, A.V., Goremykin, O.V.: Integrable systems on so(4) related with XXX spin chains with boundaries. J. Phys. A: Math. Gen. 37, 4843–4849 (2004)
Sokolov, V.V., Wolf, T.: Integrable quadratic classical Hamiltonians on so(4) and so(3,1). J. Phys. A: Mat. Gen. 39, 1915–1926 (2006)
Rumyantsev, V.V.: A comparison of three methods of constructing Lyapunov functions. J. Appl. Math. Mech. 59(6), 873–877 (1995)
Irtegov, V.D.: Invariant Manifolds of Steady-State Motions and Their Stability, Nauka, Novosibirsk (1985)
Karapetyan, A.V.: The Stability of Steady Motions, Moscow, URSS (1998)
Zubov, V.I.: Stability of integrable manifolds. Differential equations 13(9), 1720–1722 (1977)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Irtegov, V., Titorenko, T. (2009). On Invariant Manifolds of Dynamical Systems in Lie Algebras. In: Gerdt, V.P., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2009. Lecture Notes in Computer Science, vol 5743. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04103-7_14
Download citation
DOI: https://doi.org/10.1007/978-3-642-04103-7_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-04102-0
Online ISBN: 978-3-642-04103-7
eBook Packages: Computer ScienceComputer Science (R0)