Skip to main content
SpringerLink
Log in

Chaotic oscillations of spacecraft with an elastic radially oriented tether

  • Published:
Cosmic Research Aims and scope Submit manuscript

Abstract

A mechanical system consisting of a spacecraft with weightless elastic tether and load is considered in the paper. The spacecraft motion under the action of tensile force of a radially oriented tether is investigated. It is shown that elastic tether oscillations can result in appearance of chaotic modes of spacecraft motion. By means of the Melnikov method a condition is obtained, allowing one to determine the measure of damping sufficient for prevention of these chaotic modes. The influence of system’s mass-geometric and elastic characteristics on the form of phase portrait and on the value of periodic disturbance, caused by oscillations of the elastic vertical tether, is studied.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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. Beletskii, V.V. and Levin, E.M., Dinamika kosmicheskikh trosovykh sistem (Dynamics of Space Tethered Systems), Moscow: Nauka, 1990.

    Google Scholar 

  2. Zimmermann, F., Schottle, U.M., and Messerschmid, E., Optimization of the Tether-Assisted Return Mission of a Guided Re-Entry Capsule, Aerospace Science and Technology, 2005, no. 9, pp. 713–721.

  3. Beletskii, V.V., Ivanov, M.B., and Otstavnov, E.I., Model Problem of a Space Elevator, Kosm. Issled., 2005, vol. 43, no. 2, pp. 157–160. [Cosmic Research, p. 152].

    Google Scholar 

  4. Williams, P., Blanksbya, C., Trivailoa, P., and Fujii, H.A., In-Plane Payload Capture Using Tethers, Acta Astronaut., 2005, vol. 57, pp. 772–787.

    Article  ADS  Google Scholar 

  5. Ziegler, S.W. and Cartmell, M.P., Using Motorized Tethers for Payload Orbital Transfer, J. Spacecr. Rockets, 2001, vol. 38, no. 6, pp. 904–913.

    Article  ADS  Google Scholar 

  6. McCoy, J.E., Electrodynamic Tethers, Proc. 35th Intern. Astronautical Congress, Lausanne, Switzerland, October 7–13, 1984, pp. 84–440.

  7. Sorensen, K., Momentum Exchange Electrodynamic Reboost Tether. Technology Assessment Group Final Report, Space Propulsion Technologies Program, July 24, 2003, NASA Marshall Space Flight Center, Huntsville, AL 35812, 2003.

    Google Scholar 

  8. Bombardelli, C., Lorenzini, E.C., and Quadrelli, M.B., Retargetting Dynamics of a Linear Tethered Interferometer, J. Guidance Control Dynam., 2004, vol. 27, no. 6, pp. 1061–1067.

    Article  Google Scholar 

  9. Nordley, G., Tether-Tossed Mars Mission Examples, Proceed. of the 37th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit [AIAA 2001-3375], 2001.

  10. Eiden, M. and Cartmell, M.P., Overcoming the Challenges: Tether Systems Roadmap for Space Transportation Applications, Proceed. of the AIAA/ICAS Intern. Air and Space Symposium and Exposition, Dayton, 14–17 July, 2003 [AIAA 2003-2840].

  11. Ivanov, V.A., Tethered Systems in Space, Aviats. Kosmonavtika, 1984, no. 5, pp. 43–44.

  12. Cartmell, M.P. and McKenzie, D.J., A Review of Space Tether Research, Progress in Aerospace Sciences, 2008, vol. 44, pp. 1–21.

    Article  ADS  Google Scholar 

  13. Aslanov, V.S., Ledkov, A.S., and Stratilatov, N.R., Spatial Motion of a Space Tethered System Designed to Deliver Payload to the Earth, Polyot, 2007, no. 2, pp. 28–33.

  14. Sazonov, V.V., Mathematical Modeling of Deployment of a Tethered System Taking the Tether Mass into Account, Preprint of Keldysh Inst. of Applied Math., Russ. Acad. Sci., Moscow, 2006.

  15. Dignat, F. and Shilen, V., Control of Vibrations of an Orbital Tethered System, Prikl. Mat. Mekh., 2000, vol. 64, no. 5, pp. 747–754.

    MATH  Google Scholar 

  16. Aslanov, V.S., Ledkov, A.S., and Stratilatov, N.R., Influence of Tethered System of a Cargo Spacecraft on Its Attitude Motion, Polyot, 2009, no. 1, pp. 54–60.

  17. Pirozhenko, A.V., Chaotic Regimes of Motion in Dynamics of Space Tethered Systems: 2. Mechanical Aspect of Phenomena, Kosmichna Nauka i Tekhnol., 2001, vol. 7, no. 2/3, pp. 90–99.

    Google Scholar 

  18. Mel’nikov, V.K., Stability of the Center at Time-Periodic Disturbances, Trudy Moskovskogo Matematicheskogo Obshchestva, 1963, vol. 12, pp. 1–57.

    MATH  Google Scholar 

  19. Sadov, Yu.A., Forms of Equilibria of a Flexible Tether in the Plane of a Circular Orbit: 0- and 1-Parametric Families, Preprint of Keldysh Inst. of Applied Math., Russ. Acad. Sci., Moscow, 2001, no. 68.

  20. Beletskii, V.V., Dvizhenie iskusstvennogo sputnika otnositel’no tsentra mass (Artificial Satellite Motion Relative to Its Center of Mass), Moscow: Nauka, 1965.

    Google Scholar 

  21. Williams, P., Hyslop, A., Stelzer, M., and Kruijff, M., Yes-2 Optimal Trajectories in Presence of Eccentricity and Aerodynamic Drag, Acta Astronaut., 2009, no. 64, pp. 745–769.

  22. Pirozhenko, A.V. and Khramov, D.A., A Scheme of Gravitational Stabilization of a Space Tethered System with a Spherical Hinge, Tekhnicheskaya Mekhanika, 2001, no. 1, pp. 136–148.

Download references

Author information

Authors and Affiliations

  1. Samara State Aerospace University, Moskovskoye sh. 34, Samara, 443086, Russia

    V. S. Aslanov & A. S. Ledkov

Authors
  1. V. S. Aslanov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. S. Ledkov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. S. Aslanov.

Additional information

Original Russian Text © V.S. Aslanov, A.S. Ledkov, 2012, published in Kosmicheskie Issledovaniya, 2012, Vol. 50, No. 2, pp. 194–204.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Aslanov, V.S., Ledkov, A.S. Chaotic oscillations of spacecraft with an elastic radially oriented tether. Cosmic Res 50, 188–198 (2012). https://doi.org/10.1134/S0010952512020013

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0010952512020013

Keywords

Search

Navigation