Dynamic Analysis of a Light Structure in Outer Space: Short Electrodynamic Tether

The SET (short electrodynamic tether) is an extremely flexible deployable structure. Unlike most other tethers that orbit with their axis of smallest moment of inertia pointing towards the Earth's center (natural position), the SET must orbit with its axis of smallest inertia normal to the orbit plane. The Faraday effect allows the SET to modify its orbit in this position. This is due to the interaction of the Earth's magnetic field with the tether, which is an electric conductor. In order to maintain the aforementioned operating position, the SET is subjected to a spin velocity around its axis of smallest inertia. If the system were rigid, the generated gyroscopic pairs would guarantee the system's stability.The tether is not perfectly straight after deployment. This fact could make the rotation of the structure unstable. The problem is similar to the instability of unbalanced rotors. The linear study of unbalanced systems predicts the structural instability once a certain critical velocity is exceeded. Instability is due to internal damping forces. The spin velocity of the SET is greater than the critical velocity. Nevertheless, certain works that include the geometric nonlinearities show a stable behavior under such conditions. The object of this paper is to try to verify these results for the SET.The SET consists of a 100-meter tether with a concentrated mass at its end. The system has been modeled using the floating reference frame approach with natural coordinates. The substructuring technique is used to include nonlinearities in the system.

[1]  John S. Maybee,et al.  External and material damped three dimensional rotor system , 1970 .

[2]  Javier Cuadrado,et al.  A comparison in terms of accuracy and efficiency between a MBS dynamic formulation with stress analysis and a non‐linear FEA code , 2001 .

[3]  J. Cuadrado,et al.  FLEXIBLE MECHANISMS THROUGH NATURAL COORDINATES AND COMPONENT SYNTHESIS : AN APPROACH FULLY COMPATIBLE WITH THE RIGID CASE , 1996 .

[4]  Eduardo Ahedo,et al.  Analysis of Bare-Tether Systems for Deorbiting Low-Earth-Orbit Satellites , 2002 .

[5]  Ahmed A. Shabana,et al.  APPLICATION OF THE ABSOLUTE NODAL CO-ORDINATE FORMULATION TO MULTIBODY SYSTEM DYNAMICS , 1997 .

[6]  Javier García de Jalón,et al.  Kinematic and Dynamic Simulation of Multibody Systems: The Real Time Challenge , 1994 .

[7]  J. Maybee,et al.  Stability in the three dimensional whirling problem , 1969 .

[8]  Vinod J. Modi,et al.  EXPERIMENTAL INVESTIGATION OF THE DYNAMICS OF SPINNING TETHERED BODIES , 1996 .

[9]  E. Haug,et al.  Geometric non‐linear substructuring for dynamics of flexible mechanical systems , 1988 .

[10]  George Tyc,et al.  Damped Gyroscopic Modes of Spinning Tethered Space Vehicles with Flexible Booms , 1997 .

[11]  Javier Cuadrado,et al.  Modeling and Solution Methods for Efficient Real-Time Simulation of Multibody Dynamics , 1997 .

[12]  M. Géradin,et al.  Flexible Multibody Dynamics: A Finite Element Approach , 2001 .

[13]  J. Maybee,et al.  The role of material damping in the stability of rotating systems , 1972 .