Skip to main content
SpringerLink
Log in

On the sub-Riemannian geodesic flow for the Goursat distribution

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

Abstract

Under consideration is the sub-Riemannian geodesic flow for the Goursat distribution. We find the level surfaces of the first integrals that are in involution and study the trajectories in the phase space whose projections to the horizontal plane are closed curves.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Agrachev A. A. and Sachkov Yu. L., Control Theory from the Geometric Viewpoint, Springer-Verlag, Berlin (2004).

    Book  MATH  Google Scholar 

  2. Robot Motion Planning and Control (ed. J. P. Laumond), Springer-Verlag, Berlin; Heidelberg (1998).

  3. Pontryagin L. S., Boltyanskiĭ V. G., Gamkrelidze R. V., and Mishchenko E. F., Mathematical Theory of Optimal Processes [in Russian], Fizmatgiz, Moscow (1961).

    Google Scholar 

  4. Taimanov I. A., “Integrable geodesic flows of nonholonomic metrics,” J. Dyn. Control Sist., 3, No. 1, 129–147 (2003).

    Article  MathSciNet  MATH  Google Scholar 

  5. Mazhitova A. D., “The geodesic flow of a sub-Riemannian metric on a three-dimensional solvable Lie group,” Sib. Adv. Math., 23, No. 2, 99–105 (2013).

    Article  Google Scholar 

  6. Sachkov Yu. L., “Control theory on Lie groups,” J. Math. Sci., 156, No. 3, 381–439 (2009).

    Article  MathSciNet  MATH  Google Scholar 

  7. Ardentov A. A. and Sachkov Yu. L., “Extremal trajectories in a nilpotent sub-Riemannian problem on the Engel group,” Sb. Math., 202, No. 11, 1593–1615 (2011).

    Article  MathSciNet  MATH  Google Scholar 

  8. Anzaldo-Meneses A. and Monroy-Perez F., “Goursat distribution and sub-Riemannian structures,” J. Math. Phys., 44, No. 12, 6101–6111 (2003).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk Russia Novosibirsk State University, Novosibirsk, Russia

    S. V. Agapov

Authors
  1. S. V. Agapov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. V. Agapov.

Additional information

Novosibirsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 57, No. 1, pp. 3–9, January–February, 2016; DOI: 10.17377/smzh.2016.57.101

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Agapov, S.V. On the sub-Riemannian geodesic flow for the Goursat distribution. Sib Math J 57, 1–6 (2016). https://doi.org/10.1134/S0037446616010018

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0037446616010018

Keywords

Search

Navigation