Normal Mode Solution for the Vibrational Motions of Long Flexible Booms on the RAE Satellite

A normal mode analysis is applied to the Radio Astronomy Explorer satellite which uses four 750 ft booms arranged in an “X” configuration. The state variables consist of three Euler angles of the central body, a damper boom angle and “8n” generalized coordinate for the four booms, in two orthogonal directions each, for each of the “n” normal modes selected. The following information is obtained from a computer solution: (a) the static deflection of the antenna booms, (b) the natural frequencies of the configuration, and (c) the steady-state dynamic deflections of the booms due to thermal bending. Results are compared with other approaches found in the literature.