## 1 Introduction: Previous Research on Momentum-Transfer Tethers
The LEO bolo can even operate the propellant-free, extracting momentum necessary for orbital transfer from the momentum of bodies in higher orbits. Unfortunately, around the Earth, the only such body is the moon, and series of tethers able to handle at least 1.6 km/s tip speed are necessary for harnessing the orbital momentum of the moon rocks. An example of momentum-neutral tether design may be found in [12]. Even for sub-km/s delta-v offered by bolo configurations built with existing materials, a MXER (magnetic-exchange electrodynamic reboost) drive option [10] still exists. But MXER is highly speculative research; [PERSON], in 2003 [10], lists several components of the MXER bolo as having a NASA TRL (technology readiness level) equal to 3 (only proof-of concept available), and two key technologies (tether coating and tether libration control) having a TRL equal to 2 (only technology concept was formulated). In addition, a high degree of difficulty (III) in R&D is expected for many components. Therefore, alternative engineering approaches to M first. The author favors modern ion motors as near-term alternatives to momentum-neutral or MXER systems. The problem of rotating bolo (rotovator) stability has been extensively discussed by the research community. In 1996, [PERSON] [13] described an extreme wealth of rotating tether vibration types. Such vibrations may easily result in tether straying from the correct capture or release point, or may even result in tether breakage. Therefore, two parametric measures should be taken. Firstly, a material with low accumulation of elastic energy (_i.e._, high rigidity) should be used for the tether. Secondly, a damper should be used as most rigid materials themselves have very low internal mechanical energy dissipation. In 1995, [PERSON] [14] stated that, even after implementation of critical dampening, peak load due to tether vibrations exceeds steady-state load by 50%. Of course, aero-capture, as in [14], is the worst case, in terms of vibration excitation, but some vibration will be excited in the LEO bolo, as well, with each dip of the tether arm in the deeper layers of atmosphere. Even changes of tether temperature due to entering sunlight or shadow may result in vibration, which ultimately must be damped. In 1995, [PERSON] [15] speculated that large flexible booms attached to the tether, OEDIPUS-A, acted as a surprisingly effective dampening mechanism because of their high-frequency, high-strain whipping oscillations induced by the oscillations of the tether. In 1997, [PERSON] [16] proposed and experimentally verified the stability criteria for a rotating tether holding a payload. His findings can be summarized as a statement of vibration instability of any tether that is too long or rotating too slowly. Both, faster rotation and smaller length contribute to larger natural dampening factors. In 1991, [PERSON] [17] demonstrated that tether dampening is rather ineffective in suppressing fundamental transverse (libration) mode (approximately a period of 400 s for an 80 km tether), although modes with higher frequency, including longitudinal vibration modes, can be effectively suppressed. Therefore, it is important for a tether system to avoid periodic forcing at or near fundamental transverse mode frequency. Such periodic forcing may happen due to atmospheric interaction as soon as the tether tip dips into the more dense atmospheric layers. In 2003, [PERSON] [18] stated that although librations of uncontrolled tethers on elliptical orbits are inevitable, with periodic thrust applied on the tether tips, these librations can be suppressed in cases of massless tethers. In addition, [PERSON] [18] found the steady-state rotating tether solution similar to that described in Section 2, but did not quantify it. By a superposition principle, stabilization of a librating massive tether on an elliptical orbit may require a  
Figure 1: Orbital geometry of the LEO bolo (rotovator) launch assistance mission.