Skip to main content
SpringerLink
Log in

Symmetries, Reduction and Relative Equilibria for a Gyrostat in the Three-body Problem

  • Published:
Celestial Mechanics and Dynamical Astronomy Aims and scope Submit manuscript

Abstract

The problem of three bodies when one of them is a gyrostat is considered. Using the symmetries of the system we carry out two reductions. Global considerations about the conditions for relative equilibria are made. Finally, we restrict to an approximated model of the dynamics and a complete study of the relative equilibria is made.

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

  • Cid, R. and Vigueras, A.: 1985, ‘About the problem of motion of N gyrostats: I. the first integrals’, Celest. Mech. & Dyn. Astr. 36, 155-162.

    Google Scholar 

  • Duboshin, G. N.: 1984, ‘The problem of three rigid bodies’, Celest. Mech. & Dyn. Astr. 33, 31-47.

    Google Scholar 

  • Fanny, C. and Badaoui, E.: 1997, ‘Relative equilibrium in the three-body problem with a rigid body’, Celest. Mech. & Dyn. Astr. 69, 293-315.

    Google Scholar 

  • Ferrer, S., Mondéjar, F. and Vigueras, A.: 2001 (in preparation).

  • Maciejewski, A.: 1995, ‘Reduction, relative equilibria and potential in the two rigid bodies problem’, Celest. Mech. & Dyn. Astr. 63, 1-28.

    Google Scholar 

  • Marsden, J. E.: 1992, Lectures on Mechanics, L. M. S., Lectures Note Series 174, Cambridge University Press.

  • Marsden, J. E., Ratiu, T. S. and Weinstein, A.: 1984a, ‘Semidirect products and reductions in mechanics’, Trans. AMS 281, 147-177.

    Google Scholar 

  • Marsden, J. E., Ratiu, T. S. and Weinstein, A.: 1984b, ‘Reduction and Hamiltonian structures on duals of semidirect product Lie algebras’, Cont. Math. AMS 28, 55-100.

    Google Scholar 

  • Marsden, J. E. and Weinstein, A.: 1974, ‘Reduction of symplectic manifolds with symmetry’, Rep. Math. Phys. 5, 121-130.

    Google Scholar 

  • Mondéjar, F. and Vigueras, A.: 1999, ‘The Hamiltonian dynamics of the two gyrostats problem’, Celest. Mech. & Dyn. Astr. 73, 303-312.

    Google Scholar 

  • Vidiakin, V. V.: 1977, ‘Euler Solutions in the problem of translational-rotational motion of three-rigid bodies’, Celest. Mech. & Dyn. Astr. 16, 509-526.

    Google Scholar 

  • Wang, L.-S., Lian, K.-Y. and Chen, P.-T.: 1995, ‘Steady motions of gyrostat satellites and their stability’, IEEE Trans Automatic Control 40(10), 1732-1743.

    Google Scholar 

  • Wang, L.-S., Krishnaprasad, P. S. and Maddocks, J. H.: 1991, ‘Hamiltonian dynamics of a rigid body in a central gravitational field’, Celest. Mech. & Dyn. Astr. 50, 349-386.

    Google Scholar 

  • Zhuravlev, S. G. and Petrutskii, A. A.: 1990, ‘Current state of the problem of translational-rotational motion of three-rigid bodies’, Soviet Astron. 34, 299-304.

    Google Scholar 

Download references

Authors
  1. F. Mondéjar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Vigueras
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. Ferrer
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mondéjar, F., Vigueras, A. & Ferrer, S. Symmetries, Reduction and Relative Equilibria for a Gyrostat in the Three-body Problem. Celestial Mechanics and Dynamical Astronomy 81, 45–50 (2001). https://doi.org/10.1023/A:1013303002722

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1013303002722

Search

Navigation