Skip to main content
SpringerLink
Log in

Equilibrium Configurations of Tethered Three-Body Systems and Their Stability

  • Published:
The Journal of the Astronautical Sciences Aims and scope Submit manuscript

Abstract

The paper considers planar motion of a three-body tethered system whose center of mass moves in a circular orbit around the Earth. The equilibrium configurations of the system and their stability are examined and contrasted with those of the classical circular restricted three-body problem. It is observed that there are four classes of equilibrium configurations of tethered three-body systems: in two of them the bodies are collinear, while in the other two, the bodies lie in a triangular configuration. Analysis of the stability of these equilibrium configurations shows that the triangular configurations are unstable, while one of the collinear configurations (the one along the local vertical) is stable. An integral of motion is obtained, which turns out to be the Hamiltonian of the system per unit mass. The zero-velocity curves based on this Hamiltonian are presented.

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. PENZO, P. A. and AMMANN, P. W. Tethers in Space Handbook, 2nd Edition, NASA Office of Space Flight, Washington, D.C., May 1989.

    Google Scholar 

  2. LORENZINI, E. C. “A Three-Mass Tethered System for Micro-g/Variable-g Applications,” Journal of Guidance, Control, and Dynamics, Vol. 10, 1987, pp. 242–249.

    Article  Google Scholar 

  3. MISRA, A. K., AMIER, Z. E. and MODI, V. J. “Attitude Dynamics of Three-Body Tethered Systems,” Acta Astronautica, Vol. 17, No. 10, 1988, pp. 1059–1068.

    Article  Google Scholar 

  4. COSMO, M., LORENZINI, E. C., VETRELLA, S. and MOCCIA, A. “Transient Dynamics of the Tether Elevator/Crawler System,” Proceedings of the AIAA/AAS Astrodynamics Conference, Minneapolis, Minn., August 15–17, 1988, pp. 480–489.

  5. MISRA, A. K. and MODI, V. J. “Three-Dimensional Dynamics and Control of Tether-Connected N-Body Systems,” Acta Astronautica, Vol. 26, No. 2, 1992, pp. 77–84.

    Article  Google Scholar 

  6. KESHMIRI, M., MISRA, A. K. and MODI, V. J. “General Formulation for N-Body Tethered Satellite System Dynamics,” Journal of Guidance, Control, and Dynamics, Vol. 19, No. 1, 1996, pp. 75–83.

  7. SZEBEHELY, V. Theory of Orbits, The Restricted Problem of Three Bodies, New York: Academic Press, 1967.

    MATH  Google Scholar 

  8. MEIROVITCH, L. Introduction to Dynamics and Control, New York: Wiley, 1985.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, McGill University, Montreal, QC, H3A 2K6, Canada

    Arun K. Misra (Professor)

Authors
  1. Arun K. Misra
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Misra, A.K. Equilibrium Configurations of Tethered Three-Body Systems and Their Stability. J of Astronaut Sci 50, 241–253 (2002). https://doi.org/10.1007/BF03546250

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03546250

Search

Navigation