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A. Steindl, H. Troger:
"Is the Sky-Hook Configuration Stable";
Nonlinear Dynamics, 40 (2005), 4; 419 - 431.

The sky-hook, that is a string forming a connection from the surface
of the Earth to a
satellite in geostationary orbit, which may be used as track for an
Earth to space elevator, is an old dream of mankind,
originating about 100 years ago in Russia. Besides the question of
feasibility from a technological point of view
also the question concerning the stability of such a
configuration has not yet been completely solved.
Under the assumption that a proper material (carbon
nanotubes) is available making the connection possible
technologically, we address the question of stability
of the radial relative equilibrium of a tapered string reaching from
the surface of the Earth to a satellite on a
circular geosynchronous orbit around the Earth.

http://aleph.ub.tuwien.ac.at/F?base=tuw01&func=find-c&ccl_term=AC05936818

http://www.springerlink.com/openurl.asp?genre=article&eissn=1573-269X&volume=40&issue=4&spage=419