Abstract
One of the most important operations during a tethered satellite system mission is the deployment of a subsatellite from a space ship. We restrict tothe simple but practically important case that the system ismoving on a circular orbit around the Earth. The main problem duringdeployment due to gravity gradient is that the two satellites do not move along the straight radial relative equilibrium position which is stable for a tether of constant length. Instead, deploymentleads to an unstable motion with respect to the radial relativeequilibrium configuration. Therefore we introduce an optimal control strategy using theMaximum Principle to achieve a force controlled deployment of the tethered subsatellite from the radial relative equilibrium position close to the space ship to the radial relative equilibrium position far away from the space ship.
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References
Abdel-Rahman, E. M. and Nayfeh, A. H., 'Pendulation reduction in boom cranes using cable length manipulation', Nonlinear Dynamics 27, 2002, 255–269.
Bainum, P. and Kumar, V. K., 'Optimal control of the shuttle-tethered-subsatellite system', Acta Astronautica 7, 1980, 1333–1348.
Barkow, B., Steindl, A., Troger, H., and Wiedermann, G., 'Some methods of controlling the deployment of a tethered satellite', International Journal of Vibration and Control, 2003, to appear.
Beardsley, T., 'The way to go in space', Scientific American, February, 1999, 40–77.
Beletsky, V. V. and Levin, E. M., Dynamics of Space Tether Systems, Advances of the Astronautical Sciences, Vol. 83, 1993.
Bryson, A. E. and Ho, Y. C., Applied Optimal Control, Ginn and Company, Waltham, MA, 1969.
Chernousko, F. L., 'Dynamics of retrieval of a space tethered system', Journal of Applied Mathematics and Mechanics 59, 1995, 165–173.
Feichtinger, R. and Hartl, R., Optimale Kontrolle ökonomischer Prozesse, de Gruyter, Berlin, 1986.
Gilmore, R., Catastrophe Theory for Scientists and Engineers, Wiley, New York, 1981.
Hoyt, R. P., Forward, R. L., Nordley, G. D., and Uphoff, C. W., 'Rapid interplanetary tether transport systems', in Proceedings of 50th IAF Congress, Amsterdam, 1999, IAF-99-A.5.10, 31 pp.
Kirk, D. E., Optimal Control Theory, An Introduction, Network Series, Prentice Hall, Englewood Cliffs, NJ, 1970.
Krupa, M., Kuhn, A., Poth, W., Schagerl, M., Steindl, A., Steiner, W., Troger, H., and Wiedermann, G., 'Tethered satellite systems: A new concept of space flight', European Journal of Mechanics. A Solids 19, 2000, S145–S164.
Leitmann, G., An Introduction to Optimal Control, McGraw-Hill, New York, 1966.
Misra, A. K. and Modi, V. J., 'Deployment and retrieval of shuttle supported tethered satellites', Journal of Guidance and Control 5, 1982, 278–285.
Oberle, H. J., Grimm, W., and Berger, E., 'BNDSCO, Rechenprogramm zur Lösung beschränkter optimaler Steuerungsprobleme', Benutzeranleitung, TU München, Report No. M8509, 1985.
Oberle, H. J. and Opfer, G., 'Optimale Steuerung, Einführung in die Theorie und numerische Verfahren', Hamburger Beiträge zur Angewandten Mathematik, Reihe B, Bericht 13, 1989.
Proceedings of the Fourth International Conference on Tethers in Space, Science and Technology Corporation, Hampton, VA, 1995.
Seydel, R., 'A continuation algorithm with step control', in Numerical Methods for Bifurcation Problems, ISNM 70, T. Küpper, H. D. Mittelmann, and H. Weber (eds.), Birkhäuser, Basel, 1984, pp. 480–494.
Steiner, W., Steindl, A., and Troger, H., 'Dynamics of a space tethered satellite system with two rigid endbodies', in Proceedings of the Fourth International Conference on Tethers in Space, (ed.), Science and Technology Corporation, Hampton, VA, 1995, pp. 1367–1379.
Steiner, W., Steindl, A., and Troger, H., 'Center manifold approach to the control of a tethered satellite system', Applied Mathematics and Computation 70, 1995, 315–327.
Wiedermann, G., Schagerl, M., Steindl A., and Troger, H., 'Computation of force controlled deployment and retrieval of a tethered satellite system by the finite element method', in Proceedings of ECCM'99, W. Wunderlich (ed.), TU-München, 1999, pp. 410–429.
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Steindl, A., Troger, H. Optimal Control of Deployment of a Tethered Subsatellite. Nonlinear Dynamics 31, 257–274 (2003). https://doi.org/10.1023/A:1022956002484
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DOI: https://doi.org/10.1023/A:1022956002484