Skip to main content
Log in

Integrable systems with linear periodic integral for the Lie algebra e(3)

  • Published:
Lobachevskii Journal of Mathematics Aims and scope Submit manuscript

Abstract

Integrable systems with a linear periodic integral for the Lie algebra e(3) are considered. One investigates singularities of the Liouville foliation, bifurcation diagram of the momentum mapping, transformations of Liouville tori, topology of isoenergy surfaces and other topological properties of such systems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. A. V. Bolsinov and A. T. Fomenko, Integrable Hamiltonian Systems: Geometry, Topology, Classification (CRC, Boca Raton, FL, 2004).

    MATH  Google Scholar 

  2. A. V. Borisov and I. S. Mamaev, Rigid Body Dynamics (NIC Regular Chaotic Dynamics, Moscow, Izhevsk, 2001) [in Russian].

    MATH  Google Scholar 

  3. A. A. Oshemkov, “Fomenko invariants for the main integrable cases of the rigid body motion equations,” in Topological Classification of Integrable Systems, Adv. Sov. Math. 6, 67–146 (1991).

    MathSciNet  MATH  Google Scholar 

  4. A. V. Bolsinov, A. M. Izosimov, A. Yu. Konjaev, and A. A. Oshemkov, “Algebra and topology of integrable systems. Research problems,” Tr. Sem. Vektor. Tenzor. Anal. 28, 119–191 (2012).

    Google Scholar 

  5. E. O. Kantonistova, “Topological classification of integrable Hamiltonian systems in a potential field on surfaces of revolution,” Mathematics 207, 358–399 (2016).

    MathSciNet  MATH  Google Scholar 

  6. B. S. Kruglikov,“Topological classification of Leggett systems in an integrable case for 3He-A,” Russ. Math. Surv. 46, 179–181 (1991).

    Article  Google Scholar 

  7. M. Yu. Ivochkin, “Topological analysis of the motion of an ellipsoid on a smooth plane,” Sb.: Math. 199, 871–890 (2008).

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to I. Kozlov.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kozlov, I., Oshemkov, A. Integrable systems with linear periodic integral for the Lie algebra e(3). Lobachevskii J Math 38, 1014–1026 (2017). https://doi.org/10.1134/S1995080217060063

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1995080217060063

Keywords and phrases

Navigation