One of the promising technology to economize satellite communication system is the multi-beam system. The multi-beam satellite communication system requires large diameter satellite antenna. In order to satisfy several requirements, the large antenna learns to have low natural frequencies of about 1-2Hz or lower. The effects of the low frequency structural vibration on satellite attitude control have been discussed. In those effects the coupling coefficients, which shows the coupling between the rigid motion and the vibration, are important. But most of them are dealing with the flexible appendages which are connected to the satellite main body at one point. So those formulations of flexible satellite can be applied to a satellite with one-point connection. However, from the point of structural stability, it is desirable that the communication antenna reflector has multiple connection points to the main body. Using Lagrange multiplier, we revealed that the coupling coefficients are derived only by modal momentum and modal angular momentum regardless of the number of connecting points.
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