A Preliminary Investigation of the Motion of a Long, Flexible Wire in Orbit
RAND CORP SANTA MONICA CA
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This memorandum is concerned with the motion of a long, flexible wire in orbit. The wire is approximated by n point masses joined by massless rigid rods. Under the assumption of an inverse square gravitational field, the general equations of motion of the n masses are developed. Then, with all external forces except gravity neglected, and with the motion of the wire restricted to the orbital plane, two specific cases are examined. In the first case the wire spins about its center of mass, after having been initially extended in some fashion. The second case examines the motion of an extended wire which, initially, is approximately aligned with the vertical. The analysis indicates that, in the absence of internal dissipative forces, the straight-line configuration of the spinning wire is not stable, since a parametric resonance condition exists. In the second case the wire will oscillate about the vertical if the initial disturbances are small.
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