The deployment of a subsatellite from a mother spaceship moving on a circular orbit is a delicate operation for a tethered satellite system because this process leads to an unstable motion with respect to the stable radial relative equilibrium of such a system if the tether length is kept constant. Therefore, simulation tools for the implementation of stabilizing control are needed. Usually linear control, for example Kissel's law, is implemented. In this paper, we introduce an optimal control strategy to simulate the force controlled deployment of a tethered satellite from a spaceship. We compare this strategy with free deployment, deployment controlled by Kissel's law and an approach making use of the concept of “targeting” used in the controlling chaos approach.
Bainum, P. and Kumar, V.K., 1980, “Optimal control of the shuttle-tethered-subsatellite system”, Acta Astronautica7, 1333-1348.
2.
Beardsley, T., 1999, “The way to go in space”, Scientific AmericanFebruary, 40-77.
3.
Beletsky, V.V. and Levin, E.M., 1993, Dynamics of Space Tether Systems, Advances in the Astronautical Sciences Vol. 83, Univelt, San Diego, CA.
4.
Chernousko, F.L., 1995, “Dynamics of Retrieval of a Space Tethered System”, Journal of Applied Mathematics and Mechanics59, 165-173.
5.
Crellin, E.B., Janssens, F., Poelaert, D., Steiner, W., and Troger, H., 1997, “On Balance and Variational Formulations of the Equations of Motion of a Body Deploying Along a Cable”, Journal of Applied Mechanics64, 369-374.
6.
Feichtinger, R., and Hartl, R., 1986, Optimale Kontrolle ökonomischer Prozesse, Walter de Gruyter, Berlin.
7.
Handbook, 1986, “Tethers in space”, in Proceedings of the first International Conference on Tethers in Space, Sept 17-19, Arlington, VA.
8.
Handbook, 1988, Space Tethers for Science in the Space Station Era, Societa Italiana di Fisica, Conference Proceedings, 14, Bologna.
9.
Hoyt, R.P., Forward R.L., Nordley, G.D., and Uphoff, C.W., 1999, “Rapid interplanetary tether transport systems”, IAF-99-A.5.10, 50th IAF Congress Amsterdam, 31 pages.
10.
Kohler, P., Maag, W., Wehrli, R., Weber, R., and Brauchli, H., 1978, “Dynamics of a system of two satellites connected by a deployable and extensible tether of finite mass”, ESTEC Contract No 2992/76/NL/AK(SC).
11.
Krupa, M., Kuhn, A., Poth, W., Schagerl M., Steindl, A., Steiner, W., Troger H., and Wiedermann, G., 2000, “Tethered satellite systems: a new concept of space flight”, European Journal of Mechanics and Solids19, S145-S164.
12.
Leitmann, G., 1966, An Introduction to Optimal Control, McGraw-Hill, New York.
13.
Lur'e, L., 1968, Méchanique Analytique, Vols I and II, Masson and Cie, Paris.
14.
Misra, A. K. and Modi, V. J., 1982, “Deployment and retrieval of shuttle supported tethered satellites”, Journal of Guidance and Control5, 278-285.
15.
Oberle, H. J., Grimm, W., and Berger, E., 1985, BNDSCO, “Rechenprogramm zur Lösung beschränkter optimaler Steuerungsprobleme”, Benutzeranleitung, TU München, Report No M 8509.
16.
Proceedings, 1995, Proceedings of the 4th International Conference on Tethers in Space, April 10-14, Washington DC.
17.
Solid Mechanics and its Applications, vol. 80, 345-354, Kluwer, Dortrecht.
18.
Schagerl, M., Troger, H., and Wiedermann, G., 1999, “Boundary Conditions for the Cable Dynamics of Tethered Satellite Systems”, in Proceedings of the 3rd International Symposium on Cable Dynamics, Trondheim, Norway, August 1999, pp 55-60.
19.
Seydel, R., 1984, “A continuation algorithm with step control”, in Numerical Methods for Bifurcation Problems, Birkhäuser.
20.
Steiner, W., Steindl, A., and Troger, H., 1995a, “Dynamics of a space tethered satellite system with two rigid endbodies”, in Proceedings of the 4th International Conference on Tethers in Space, Washington DC, 1994, Science and Technology Corporation, Hampton, VA, 1367-1379.
21.
Steiner, W., Steindl, A., and Troger, H., 1995b, “Center manifold approach to the control of a tethered satellite system”, Applied Mathematics and Computation70, 315-327.
22.
Steiner, W., 1998, “Transient Chaotic Oscillations of a Tethered Satellite System”, Acta Mechanica127, 155-163.
23.
Vu-Quoc, L. and Simo, J. C., 1987, “Dynamics of earth-orbiting flexible satellites with multibody components”, Journal of Guidance, Control and Dynamics10, 549-558.
24.
Wiedermann, G., Schagerl, M., Steindl A., and Troger, H., 1999, “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., 410-429.
25.
Zimmermann, F., Schoettle, U. M., and Messerschmid, E., 1999, “Optimal deployment and return trajectories for a tether-assisted re-entry mission”, AIAA paper 99-4168, vol. 66, 125-161, AIAA Atmospheric Flight Mechanics Conference, Portland, OR, August 9-11.
