Skip to main content
SpringerLink
Log in

Method of Deployment of a Tethered Space System Along the Local Vertical

  • Published:
International Applied Mechanics Aims and scope

Two bodies coupled by an elastic weightless tether in space are considered. A fundamentally new approach to solving the problem of the deployment of a tethered space system along the local vertical in a circular orbit is formulated and theoretically substantiated. This approach is based on the change-of-angular-momentum theorem. It allows programming a tether length control law that purposefully changes the angular momentum of the tether under the gravitational moment until the deployed tether is aligned with the local vertical. The deployment of a specific tether is considered as an example to demonstrate the simplicity of the approach and the way of verification of the mathematical model

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. E. M. Levin, “Deployment of a long tether in orbit,” Kosm. Issled., 21, No. 1, 678–688 (1983).

    Google Scholar 

  2. K. E. Tsiolkovsky, “Free space,” in: Collected Works [in Russian], Vol. 2, Izd.ANSSSR, Moscow (1954), pp. 26–68.

  3. K. E. Tsiolkovsky, Way to Stars (Collected Works) [in Russian], Izd. AN SSSR, Moscow (1960).

    Google Scholar 

  4. M. Akbarzade and A. Farshidianfar, “Application of the amplitude–frequency formulation to a nonlinear vibration system typified by a mass attached to a stretched wire,” Int. Appl. Mech., 50, No. 4, 476–483 (2014).

    Article  ADS  MathSciNet  Google Scholar 

  5. V. V. Beletsky, Motion of an Artificial Satellite About its Center of Mass, Israel Program for Scientific Translations, Jerusalem (1966).

  6. B. Barkow, “Controlled deployment of a tethered satellite system,” Proc. Appl. Math. Mech., No. 2, 224–225 (2003).

  7. B. Barkow, A. Steindl, H. Troger, and G. Wiedermann, “Various methods of controlling the deployment of a tethered satellite,” J. Vibr. Control, No. 9, 187–208 (2003).

  8. I. Bekey, “Tethers open new space options,” Astronautics and Aeronautics, 21, No. 4, 32–40 (1983).

    ADS  Google Scholar 

  9. I. Bekey and P. A. Penzo, “Tether propulsion,” Aerospace America, 24, No. 7, 40–43 (1986).

    Google Scholar 

  10. V. V. Beletsky and E. M. Levin, “Dynamics of space tether systems,” Adv. Astronaut. Sci. (1993).

  11. L. J. Cantafio, V. A. Chobotov, and M. G. Wolfe, “Photovoltaic gravitationaly stabilised, solid-state satellite solar power station,” J. Energy, 1, No. 6, 352–363 (1977).

    Article  Google Scholar 

  12. V. A. Chobotov, “Gravitational excitation of an extensible dumbell satellite,” J. Spacecraft and Rockets, 4, No. 10, 1295–1300 (1967).

    Article  ADS  Google Scholar 

  13. R. P. Hoyt and Ch. Uphoff, “Cislunar tether transport system,” J. Spacecraft and Rockets, 37, No. 2, 1–15 (2000).

    Google Scholar 

  14. K. R. Kroll, “Tethered propellant resupply technique for space stations,” Acta Astronautica, 12, No. 12, 987–994 (1985).

    Article  ADS  Google Scholar 

  15. E. M. Levin, Dynamic Analysis of Space Tether Missions, Univelt, San Diego (2007).

    Google Scholar 

  16. E. C. Lorenzini et al., “Acceleration levels on board the space station and a tethered elevator for micro- and variable-gravity applications,” in: Proc. 2nd Int. Conf. on Space Tethers for Science in the Space Station Era (Venice, Italy, October 4–8, 1987), A89-43326 18-12, Bologna, Societa Italiana di Fisica (1988), pp. 513–522.

  17. A. Lur’e, Analytical Mechanics, Springer, Heidelberg (2002).

    Book  Google Scholar 

  18. C. Menon, M. Kruijff, and A. Vavouliotis, “Design and testing of a space mechanism for tether deployment,” J. Spacecraft and Rockets, 44, No. 4, 927–939 (2007).

    Article  ADS  Google Scholar 

  19. V. J. Modi and A. K. Misra, “Deployment dynamics of tethered satellite systems,” AIAA Paper, No. 1398, 10 (1978).

  20. L. G. Napolitano and F. Bevilacqua, “Tethered constellations, their utilization as microgravity platforms and relevant features,” in: 35th Int. Astronautical Congr. (October 7–13, 1984), Lausanne, Switzerland (1984), pp. 84–439.

  21. D. A. Padgett and A. P. Mazzoleni, “Analysis and design for nospin tethered satellite retrieval,” J. Guidance Contr. Dyn., 30, No. 5, 1516–1519 (2007).

    Article  ADS  Google Scholar 

  22. J. Pearson, “Anchored lunar satellites for cislunar transportation and communication,” J. Astron. Sci., 17, No. 1, 39–62 (1979).

    Google Scholar 

  23. C. C. Rupp and R. R. Kissel, Tetherline System for Orbiting Satellites, U. S. Patent No. 4083520, Int. Cl. B. 64 G 1/100, US Cl. 244/167; 244/161, April II (1978).

  24. C. C. Rupp and J. H. Laue, “Shuttle/tethered satellite system,” J. Astronaut. Sci., 26, No. 1, 1–17 (1978).

    ADS  Google Scholar 

  25. W. Steiner, &. Steindl, and H. Troger, “Center manifold approach to the control of a tethered satellite system,” Appl. Math. Comp., 70, 315–327 (1995).

    Article  MathSciNet  MATH  Google Scholar 

  26. A. Steindl, W. Steiner, and H. Troger, “Optimal control of retrieval of a tethered subsatellite,” Solid Mech. Appl., 122, 441–450 (2005).

    Google Scholar 

  27. A. Steindl and H. Troger, “Optimal control of deployment of a tethered subsatellite,” Nonlin. Dynam., 31, 257–274 (2003).

    Article  MathSciNet  MATH  Google Scholar 

  28. C. J. Swet, Method for Deployment and Stabilising Orbiting Structures, U.S. Patent Office No. 3532298, Int. Cl. B 64 G 1/00, U.S. Cl. 244-1, October 6 (1970).

  29. G. Wiedermann, M. Schagerl, A. Steindl, and H. Troger, “Computation of force controlled deployment and retrieval of a tethered satellite by the finite element method,” in: ECCM ‘99 European Conf. on Computational Mechanics, Munchen, Germany, August 31–September 3 (1999), pp. 410–429.

  30. P. Williams, “Application of pseudospectral methods for receding horizon control,” J. Guidance, Contr. Dyn., 27, No. 2, 310–314 (2004).

    Article  ADS  Google Scholar 

  31. P. Williams and P. Trivailo, “On the optimal deployment and retrieval of tethered satellites,” in: 41st AIAA/ASME/SAE/ASEE Joint Propulsion Conf. and Exhibit, Tucson, July 10–13 (2005), pp. 157–163.

  32. P. Williams, “Libration control of tethered satellites in elliptical orbits,” J. Spacecraft and Rockets, 43, No. 2, 476–479 (2006).

    Article  ADS  Google Scholar 

  33. A. E. Zakrzhevskii and V. S. Khoroshilov, “Dynamics of an unstabilized spacecraft during the deployment of an elastic pantograph structure,” Int. Appl. Mech., 50, No. 3, 341–351 (2014).

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, 3 Nesterova St., Kyiv, Ukraine, 03057

    A. E. Zakrzhevskii

Authors
  1. A. E. Zakrzhevskii
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. E. Zakrzhevskii.

Additional information

Translated from Prikladnaya Mekhanika, Vol. 51, No. 6, pp. 80–93, November–December 2015.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zakrzhevskii, A.E. Method of Deployment of a Tethered Space System Along the Local Vertical. Int Appl Mech 51, 670–681 (2015). https://doi.org/10.1007/s10778-015-0724-4

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10778-015-0724-4

Keywords

Search

Navigation