Nonlinear Dynamics of Two-Body Tethered Satellite Systems: Constant Length Case
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Nonlinear Dynamics of Two-Body Tethered Satellite Systems: Constant Length Case A. K. Misra,' M. S. Nixon/ and V. J. Modi 3 Abstract The equations governing the three-dimensional motion of a two-body tethered satellite system are highly nonlinear, and their solutions are likely to exhibit interesting behavior typical to nonlinear systems. In this paper, these equations are analyzed using numerical tools such as phase portraits, spectral analysis, Poincare sections and Lyapunov exponents. Motion in the stationkeeping phase (when the tether length is constant) is studied, first considering the in-plane pitch motion only, and then considering the three-dimensional coupled pitch and roll motions. Regions of both regular (periodic or quasi-periodic) and chaotic motion are observed to exist in the planar system for only elliptic orbits, but in the case of coupled motion for both circular and elliptic orbits. The size of the chaotic region grows with eccentricity, and in the coupled motion circular orbit case with increasing values of the Hamiltonian.
Introduction A tethered satellite system consists of two or more orbiting satellites linked by a tether. Such systems have a vast potential for applications in space. They can be used for upper atmospheric experiments, to generate artificial gravity, for orbital transfer, for communication, etc. Detailed descriptions of possible applications have been given by Penzo and Ammann [1] and Cosmo and Lorenzini [2]. Several flights of space tethered systems have already taken place. TSS-l, the maiden mission of the American/Italian tethered satellite program, flew in 1992, but with limited success. The subsatellite could be deployed only up to 250 meters instead of the planned 20 km; however, the tether motion was successfully controlled. TSS-IR, the reflight mission took place in early 1996. Approximately 19 km 'Professor, Dept. of Mech. Eng., McGill University, Montreal, QC, Canada, H3A 2K6; Senior Member, AAS. 2Engineer, Space Systems, CAE Electronics Ltd., P.O. Box 1800, St. Laurent, QC, Canada, H4L 4X4. 3Professor Emeritus, Dept. of Mech. Eng., University of British Columbia, Vancouver, B.C., Canada, V6T 1Z4; Fellow, AAS.
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of tether was deployed and maintained for several hours allowing much dynamical information to be obtained; 'however, the tether snapped before the subsatellite could be retrieved. NASA also flew SEDS (Small Expendable-Tether Deployment System) I and II, in 1993 and 1994, respectively. Both missions involved successful deployment of a 20 km long tether from the second stage of an orbiting Delta II rocket and all the mission goals were achieved. One of the most successful tethered systems is the TiPS (Tether Physics and Survivability) experiment [3]. It consists of two payloads connected by a 4 km long tether and has been in orbit since June 1996. Several suborbital tethered flights have also taken place. Of note are the Canadian experiments OEDIPUS-A and C involving 1 km long tethers, launched in 1989 and 1995, respectivel
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