应用配点法的太阳帆CRTBP周期轨道设计

针对太阳帆航天器在圆形限制性三体问题(CRTBP)中人工拉格朗日点附近周期轨道的设计问题,首先分析了CRTBP中太阳帆人工拉格朗日点的存在条件和分布,然后针对大多数人工拉格朗日点附近周期轨道信息难以获取的特点,采用高阶全局配点法将原非线性方程求解问题转化为非线性规划问题,并最终得到周期轨道的近似解.运算结果表明通过该方法可以得到三维空间中人工拉格朗日点附近周期轨道,且对初始猜测值依赖程度不高,为太阳帆在高精度模型中的周期轨道设计奠定了基础.

日地系统CRTBP模型下飞行器编队的阈值控制

针对深空探测中具有一般性的圆形限制性三体(CRTBP)模型,进行主从飞行器编队建模。将控制器设计转化为一类线性矩阵不等式问题,并权衡编队系统对燃耗、精度的要求以及推进器的推力范围,设计阈值控制方案。仿真实例参考NASA预研任务,给出编队机动和保持的控制过程,表明基于所述控制方案,编队系统满足性能指标要求。

The Criteria for Reducing Centrally Restricted Three-Body Problem to Two-Body Problem

Our Solar System contains eight planets and their respective natural satellites excepting the inner two planets Mercury and Venus. A satellite hosted by a given Planet is well protected by the gravitational pertubation of much heavier planets such as Jupiter and Saturn if the natural satellite lies deep inside the respective host Planet Hill sphere. Each planet has a Hill radius aH and planet mean radius RP and the ratio R1=RP/aH. Under very low R1 (less than 0.006) the approximation of CRTBP (centrally restricted three-body problem) to two-body problem is valid and planet has spacious Hill lobe to capture a satellite and retain it. This ensures a high probability of capture of natural satellite by the given planet and Sun’s perturbation on Planet-Satellite binary can be neglected. This is the case with Earth, Mars, Jupiter, Saturn, Neptune and Uranus. But Mercury and Venus has R1=RP/aH =0.01 and 5.9862 × 10-3 respectively hence they have no satellites. There is a limit to the dimension of the captured body. It must be a much smaller body both dimensionally as well masswise. The qantitative limit is a subject of an independent study.

一种面向限制性三体问题的轨道-姿态运动模态构建方法

针对平动点附近的具有强非线性和耦合性的轨道-姿态动力学机理分析,以及如何利用其动力学特性完成相关任务操作等问题,提出了基于Floquet理论的轨道-姿态运动模态构建方法,并探讨了所构建模态的典型应用。首先,在平动点轨道-姿态周期解的基础上,对轨道-姿态状态转移矩阵进行分块,根据分块矩阵特征值特点,建立了姿态模态和姿轨耦合模态,与轨道模态共同构成完整的轨道-姿态运动模态。然后,对模态特性进行了相空间分析。最后,以平动点相对轨道-姿态运动解析、平动点轨道-姿态稳定性控制和平动点轨道附近姿轨编队设计为应用案例,相应数值仿真表明了所提出模态的正确性,以及在典型航天任务设计与控制中的应用价值。

圆型限制性三体问题下Halo-绕月轨道的星间测距定轨

在传统星座自主定轨中,SST(satellite to satellite tracking)可以同时提供轨道的大小、形状和星座相对方位信息,但不能确定星座的绝对定向。针对这一亏秩问题,联合圆型限制性三体模型CRTBP(circle restricted three bodyproblem)下的一种平动点周期轨道-Halo轨道飞行器,与二体问题轨道卫星组成扩展星座。利用两种力模型的特性差异,可以去除星座系统上的相关性,避免星座的整体旋转,从而确定星座的全部轨道状态参量。分析Halo轨道的力模型及性态特点,从系数矩阵的相关性角度讨论引进Halo轨道对定轨法矩阵正定性的改善作用,利用地月系L1平动点附近的Halo轨道与月球低轨卫星(LMO)的星间链路,在理想CRTBP框架下进行自主定轨仿真。初步验证了LMO-Halo星座定轨可行性,为开展附加平动点轨道的星座SST定轨提供了参考依据。

地月系Halo轨道族的分岔研究

讨论了利用单值矩阵的特征值研究Halo周期轨道稳定性和分岔特性的方法;建立了稳定阶数用于对周期轨道稳定性进行定性评判;系统地研究了对周期轨道拟周期分岔、正切分岔和n倍周期分岔。最后计算了地月系L1点附近Halo轨道族的稳定性和分岔,指出分岔轨道将在深空探测轨道设计中发挥独特的作用。

Port-Hamiltonian Based Control of the Sun-Earth 3D Circular Restricted Three-Body Problem: Stabilization of the <i>L</i>₁Lagrange Point

In this paper, we use Port-Hamiltonian framework to stabilize the Lagrange points in the Sun-Earth three-dimensional Circular Restricted Three-Body Problem (CRTBP). Through rewriting the CRTBP into Port-Hamiltonian framework, we are allowed to design the feedback controller through energy-shaping and dissipation injection. The closed-loop Hamiltonian is a candidate of the Lyapunov function to establish nonlinear stability of the designed equilibrium, which enlarges the application region of feedback controller compared with that based on linearized dynamics. Results show that the Port-Hamiltonian approach allows us to successfully stabilize the Lagrange points, where the Linear Quadratic Regulator (LQR) may fail. The feedback system based on Port-Hamiltonian approach is also robust against white noise in the inputs.

基于地月自由返回轨道的DRO入轨策略

大幅值逆行轨道(DRO)是地月空间中的一类周期轨道,这类轨道具有长期稳定、入轨能量低的特点,可作为未来载人月球以及载人火星任务的中转站。面向载人任务的DRO入轨问题应重点考虑任务安全性,并综合考虑飞行时间和脉冲消耗。基于地月自由返回轨道设计了两脉冲直接转移和四脉冲月球借力转移轨道。首先在圆型限制性三体模型下计算了4类自由返回轨道的解族,其次采用地心顺行月心逆行自由返回轨道,获得直接入轨和月球借力2种方式进入不同周期DRO所需的飞行时间和脉冲消耗。仿真表明:对于共振比2:1的DRO轨道,直接入轨方式所需的速度脉冲约为607 m/s,飞行时间约为6.17 d,飞行器在DRO入轨脉冲失效的情况下也可无动力返回地球。四脉冲月球借力方式所需的速度脉冲约为241 m/s,飞行时间约为14.53 d。

Universal method for designing periodic orbits by homotopy classes in the elliptic restricted three-body problem

The current methods for designing periodic orbits in the elliptic restricted three-body problem(ERTBP)have the disadvantages of targeting limited orbits and ergodic searches and considering only symmetric orbits.A universal method for designing periodic orbits is proposed in this paper.First,the homotopy classes of orbits are structured based on their topological structures.Second,a dynamic model based on homotopy classes,ranging from the circular restricted three-body problem(CRTBP)to the ERTBP,can be built using the homotopy method.Third,a multi-and a single-period orbit were selected based on the resonance ratios.Finally,the corresponding orbit in the ERTBP was computed by modifying the initial condition of the orbit in the CRTBP.This method,without an ergodic search,can extend to any orbit,including an asymmetric orbit in the CRTBP,to the ERTBP model,and the two orbits are of the same homotopy class.Examples of the Earth–Moon ERTBP are presented to verify the efficiency of this method.

共线平动点附近周期轨道的分析研究方法

首先介绍了圆型限制性三体问题的非线性常微分运动方程组,利用定性分析方法、级数解法和数值解法,系统地介绍了这个问题的求解分析方法,相应地给出了共线平动点附近的力学特性、条件周期(和拟周期)轨道,并通过分析一个周期处的状态转移矩阵(Monodromy矩阵)分析了各类轨道的稳定性以及几种周期和拟周期轨道之间的关系。另外,还给出了圆型限制型三体模型下Halo轨道的牛顿迭代算法。