面向人工重力技术的绳系自旋航天器动力学建模与分析

STUDY ON MODELING AND ANALYSIS OF A TETHERED SPINNING ARTIFICIAL GRAVITY SPACECRAFT

面向人工重力技术,对哑铃型绳系自旋航天器系统进行了动力学建模、近似解析分析和数值仿真.首先,基于凯恩方法建立了二维平面上系统动力学方程组.然后,适当选取空间和时间标尺,将系统方程去量纲化.引入系绳长度与空间标尺之比作为小参数,利用小参数摄动方法,对无量纲系统方程作了合理简化.基于椭圆积分和椭圆函数理论,对绳系系统自旋周期进行了近似解析估算.给出乘员舱内人工重力和科氏力的计算公式.数值仿真表明,合理选择系绳长度和自旋角速度,可以在乘员舱内产生适合航天员居住的人工重力,其波动幅值甚微,波动频率远离人体敏感频带,且科氏力与人工重力相比其值甚微.

The dynamic modeling,approximate analytical solutions,and numerical simulations were conducted for an dumbbell-shaped tethered spinning artificial gravity spacecraft.Firstly,the dynamic equations were derived in a 2-D plane by using Kane′s method.Then the equations were nondimensionalized by introducing proper spatial and temporal scales.The ratio of the tethering length to the spatial scale was introduced as a small parameter,and then the dimensionless equations were simplified by using the small parameter perturbation method.The spin period of the tethered system was approximately estimated based on elliptic integrals and elliptic functions.Both formulas of the artificial gravity and the Coriolis force in the crew capsule were derived.Finally,Numerical simulations were carried out.The results indicate that,by properly designing the tethering length and spin angular velocity,the fluctuation amplitude of the artificial gravity is sight,the fluctuation frequency is far away from the sensitive band of the human body,and the Coriolis force can be neglected.Therefore,the dumbbell-shaped tethered spinning spacecraft can produce an artificial gravity environment for astronauts to live in.