常值径向推力下的飞行器运动轨迹

研究了初始停泊轨道为椭圆时,空间飞行器在常值径向推力下运动的有界性和周期性.首先建立了飞行器运动的动力学方程,并通过能量积分和角动量积分进行了简化.然后将有界性的研究转化为一个一元三次不等式的求解,并在此基础上针对不同的初始真近点角分别进行了研究,得到了运动的边界和有界性条件.接下来利用椭圆积分研究了运动的周期性,分别研究了径向运动、极角转动以及整体运动的周期性.最后用数值算法得到了运动的周期轨道.

Trajectory of a spacecraft with constant radial thrust

The trajectory of a spacecraft under constant radial thrust was studied.Great deals of efforts were dedicated to investigate the boundedness and periodicity.The case of elliptic parking orbit was focused.First,the equations of motion were formulated in polar coordinates and simplified into quadratures by using of energy integral and angular momentum integral.Then,the orbital boundedness was analyzed by transforming the original problem into solving a cubic inequality.Basing on different initial parking true anomaly,the problem was researched separately.The bounds of motion and escaping conditions were obtained in terms of thrust.Next,the periodicity of motion was studied by utilizing elliptic integrals.The periodicity of radial motion and periodicity in polar angle changing were explained.A property of quasi-periodicity in motion was described.The quasi-periodic motion could degenerate into periodic orbits,if a condition among initial parking parameters and thrust were satisfied.Meanwhile,a Newton-Raphson algorithm was given to obtain periodic orbits numerically.Several numerical examples were given to support the conclusion.