绳系卫星系统耦合振动频率的确定

DETERMINATION OF FREQUENCIES OF COUPLED IN-PLANE VIBRATIONS OF GENERAL TETHERED SATELLITE SYSTEMS

将N(N≥2)体绳系卫星系统的各节系绳分为足够多的小段,如共有M-1段,每小段上的系绳张力可认为是常量。这样由N 体问题转化来的M 点问题即可逼真系绳张力沿系绳的变化。利用中间连接点的边界条件,M 点边界值问题可简化为等效的两点边界值问题,从而平面内耦合振动频率的求解归化为四阶行列式的求值。由绳系卫星系统运动中心概念推导出的每小段系绳张力的平均值,被用于系统振动频率的求解。并给出一套适合于编制计算程序的求解轨道平面内耦合振动频率的数学表达式,以及一组模拟计算结果。

Tethers of a tethered satellite system are divided into manytether segments,say M-1 segments altogether,so that the tension oneach segment can be considered as a constant By using the characteristicsof the intermediate junction points,the M-point boundary value problemcan be reduced to a two-point problem,and frequencies of coupled in-plane vibrations of the system can be determined by evaluating 4thdeterminants.By the concept of the centre of motion,an accurate expres-sion for tether tension is derived and used in determining frequencies.The method can be applied to all N-body(N≥2)tethered satellite systems.