Astronomy and Astrophysics – Astronomy
Scientific paper
Dec 1992
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992cemda..54..317b&link_type=abstract
Celestial Mechanics and Dynamical Astronomy (ISSN 0923-2958), vol. 54, no. 4, p. 317-341.
Astronomy and Astrophysics
Astronomy
2
Circular Orbits, Hill Method, Legendre Functions, Revolving, Tethering, Transverse Oscillation, Asymptotic Methods, Boundary Conditions, Equations Of Motion
Scientific paper
We analyze the transverse vibrations of a tether, modeled as an inextensible cable, and revolving at an average rate equal to the orbital rate. The reference motion is a revolving rigid tether. During this motion the force in the tether (time and location dependent) remains, in a first approximation, aligned with the tether axis. Separation of variables for the vibrations about this motion gives a Legendre equation for the spatial dependency of the deformations and Hill's equations for time dependency of the in- and out-of-plane deformations. Asymptotic expressions for the separation constant and the critical values are given. The first and second in-plane deformation mode are unstable for zero end masses. By increasing the ratio of the concentrated over the distributed mass the deformation modes can be stabilized and the values of the separation constant can be made a multiple of the distribution of the critical points. Introducing unequal tip masses does not affect this result.
Breakwell John V.
Janssens F. L.
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