Astronomy and Astrophysics – Astronomy
Scientific paper
Sep 1992
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992cemda..53..255f&link_type=abstract
Celestial Mechanics and Dynamical Astronomy (ISSN 0923-2958), vol. 53, no. 3, 1992, p. 255-266.
Astronomy and Astrophysics
Astronomy
1
Circular Orbits, Kepler Laws, Liapunov Functions, Satellite Orbits, Tethered Satellites, Coordinates, Equations Of Motion, Tetherlines, Variational Principles
Scientific paper
A problem of Liapunov's stability of relative equilibria of a flexible nonstretchable thread attached to the satellite moving in a circular Keplerian orbit in the first approximation is considered. When it is in the position of relative equilibrium, the thread is known to be situated either along the radius vector of the orbit (the 'radial' equilibrium) or along the circular orbit (the 'tangential' equilibrium) and in each case the thread can be in a 'folded' state. It is shown that 'folded radial' equilibria of the thread are always unstable while 'tangential' ones are unstable if the thread is sufficiently short in comparison with the radius of the orbit. The generalized Chetaev functional has been constructed to prove the instability.
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