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针对转移时间和始末状态固定的航天器燃耗最优轨道的求解,给出了一种延拓方法:以双脉冲轨道为初值,首先求解全程推进轨道,然后逐步增加推力幅值,应用直接/间接混合法依次求解所有推力幅值下的、满足包括开关函数在内的所有必要条件的转移轨道,包括连续和脉冲推力轨道。通过基于开关函数曲线变化趋势的开关序列预设方法,以及基于已有优化结果的延拓步长自适应方案,实现了延拓方法的自动运行。为实现该延拓方法,给出了适用于改进春分点根数模型的脉冲最优转移轨道主矢量必要条件,推导了无推力轨道段改进春分点根数协态变量状态转移矩阵。通过3个算例对延拓求解会遇到的不同情况进行了具体说明。延拓方法可以看作现有直接/间接混合法的进一步完善与拓展,延拓过程和结果有助于对燃耗最优轨道与系统参数之间的关联获得更为深刻的认识。
Aiming at solving the optimal orbit combustion optimal spacecraft with transfer time and state of arrival, a continuation method is given. Firstly, using double pulse orbit as the initial value, the full orbit is first solved, then the thrust amplitude is gradually increased, and the direct The indirect hybrid method solves, in turn, all orbital impulses that satisfy all the necessary conditions, including the switch function, for all thrust amplitudes, including continuous and impulsive thrust trajectories. Through the method of presetting the switch sequence based on the trend of the curve of the switch function curve and the adaptive algorithm of the extension step based on the existing optimization results, the continuation method is realized automatically. In order to realize this continuation method, the necessary conditions of impulse optimal transfer trajectory principal vectors which are suitable for improving the vernal equinox root number model are given, and the state transition matrix of the improved equinox number of equinoxes is derived. Three cases are used to illustrate the different situations encountered by the extension solution. The continuation method can be seen as a further improvement and expansion of the existing direct / indirect hybrid method. The continuation process and the results help to gain a deeper understanding of the correlation between the optimal fuel consumption trajectory and the system parameters.