Abstract - The transverse oscillations of a tethered system with a free end in elliptic orbit are considered. These are important in certain momentum transfer maneuvers with tethers. To first approximation, transverse and longitudinal oscillations are decoupled. The equations for the former lead to a Sturm-Liouville problem, so that the eigenvalues and eigenfunctions can be determined. A specific example is chosen to reduce the number of free parameters and provide numerical evidence for the theory developed. For this case, eigenvalues are computed and the time equations are numerically integrated for each mode, finding instabilities in some modes. Some are due to resonance, some to loss of tether tension. Small changes in the system mass distribution can improve stability.
On the stability of a tethered system with a free end in elliptic orbit
LORENZINI, ENRICO
2001
Abstract
Abstract - The transverse oscillations of a tethered system with a free end in elliptic orbit are considered. These are important in certain momentum transfer maneuvers with tethers. To first approximation, transverse and longitudinal oscillations are decoupled. The equations for the former lead to a Sturm-Liouville problem, so that the eigenvalues and eigenfunctions can be determined. A specific example is chosen to reduce the number of free parameters and provide numerical evidence for the theory developed. For this case, eigenvalues are computed and the time equations are numerically integrated for each mode, finding instabilities in some modes. Some are due to resonance, some to loss of tether tension. Small changes in the system mass distribution can improve stability.
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