地月循环轨道动力学建模与计算研究

根据地月循环轨道的概念,按照生成第二类周期轨道的弧段进行分类,并讨论了其共振性与对称性在轨道设计与应用中的作用。然后归纳了三种循环轨道的动力学建模与计算方法及其轨道延拓策略,最后总结了三种方法的利弊和应用轨道类型。对地月系统循环轨道的研究和分析,能够为我国未来载人登月工程提供一种新的思路与理论支持。     

利用连续推力的人工太阳同步轨道设计方法

针对人工太阳同步轨道的设计方法进行研究,通过施加法向连续推力调整升交点赤经（RAAN）变化率。首次推导了升交点赤经在变方向推力作用下的周期摄动平均值的精确计算公式,解决了已有近似方法对相关轨道参数的取值范围存在限制的问题,并给出了对应的轨道倾角周期摄动平均值计算公式。在分析J2项摄动对升交点赤经影响的基础上,给出了所需的法向连续推力幅值和一个轨道周期内对应的速度增量的计算方法。通过数值仿真,校验了计算公式的正确性,分析了实现人工太阳同步轨道的连续法向推力对轨道倾角的影响,给出了连续推力幅值随轨道参数的变化规律,并且提出了未来工程任务的应用建议。     

基于大幅值Lyapunov轨道稳定流形的地月转移方法

针对现有的基于不变流形地月转移轨道设计方法存在的转移时间长、需要额外速度增量的缺点,本文利用平面圆型限制性三体问题下大幅值Lyapunov轨道的稳定流形,提出了一种地月低能转移轨道设计方法。首先计算与给定近月轨道相切的大幅值Lyapunov轨道作为参考轨道;然后根据小偏差值对稳定流形的影响确定Lyapunov轨道初始点的取值范围;再通过最近点截面确定与给定近地轨道相切的Lyapunov轨道的稳定流形;最后根据稳定流形的切点调整近月轨道半径,通过一条稳定流形直接连接近地轨道与近月轨道来实现地月转移。仿真结果表明,该方法仅需要两次速度增量,在能耗较低的前提下大大减少了探测器渐近Lyapunov轨道时的飞行时间,为地月低能转移轨道的设计提供了一种新思路。     

三角平动点附近高阶解在轨道位置保持中的应用

首先给出三角平动点附近的高阶解析解,并计算了三种特殊的运动类型。以日–地+月系三角平动点附近无长周期运动分量的拟周期轨道作为目标轨道,探讨轨道保持问题。针对三角平动点任务的轨道保持问题,我们研究了两种轨道保持策略,分别为多点打靶轨道保持与重构目标轨道的策略。计算中,将轨道控制问题转化为非线性规划问题,并以优化方法求解。仿真表明优化方法在轨道保持问题求解方面非常有效。     

线性相对运动的正切拦截和正切交会轨道研究

针对冲量方向与追踪器速度方向相同的正切轨道问题,用线性相对运动方程研究了正切于初始轨道和正切于目标轨道的共面轨道拦截和轨道交会问题。得到初始和终端时刻的相对速度向量的解析表达式,定义了两个关于目标真近点角的单变量函数,于是正切拦截和正切交会问题等价于这两个函数分别等于零,最后用割线法求解这两个函数的数值解。根据能量最优要求,考虑初始漂移段,分析了一个周期内的最佳初始正切冲量点。仿真结果校验了本文提出的方法。     

降低亚轨道飞行器再入法向过载峰值的攻角设计方法

针对亚轨道飞行器再入中的大过载问题,提出一种通过保持法向过载动态平衡以大幅降低法向过载峰值的攻角设计方法。该方法基于再入飞行中过载演化特性,通过自主分段、预测反馈及迭代修正对再入攻角进行设计,使攻角变化率与法向过载的期望平衡值相适应,并可经过重复计算及收敛实现法向过载峰值最小化。仿真计算的结果表明,该方法能够大幅降低亚轨道飞行器再入中的法向过载,且按照该方法设计所获攻角策略可有效用于亚轨道飞行器再入任务规划、再入轨迹和制导律设计。
     

环月飞行器返回轨道设计与优化

针对传统月地返回轨道设计方法在从初始轨道直接转移的局限性,提出一种基于Lambert问题的月地转移轨道设计方法。该方法重新选取了轨道约束参数,并在笛卡尔坐标系下建立了返回轨道动力学模型,并基于该模型全面分析了返回轨道关于约束参数的变化特性。此外,针对带有约束条件的返回轨道优化设计问题,提出了快速收敛的函数构造法,并给出了有效的目标函数形式。以某一在轨环月飞行器的轨道参数作为初始轨道进行返回轨道计算,结果验证了所提出返回轨道设计方法以及函数构造法的有效性。     

小脉冲约束下的近圆轨道控制方法研究

对于近圆轨道平面内参数的控制,采用传统的双脉冲控制方法,一条轨道圈内至多只能进行两次轨道控制,在单次控制小脉冲约束下,整个控制周期会很长。文章针对单次控制小脉冲约束,提出了一种增加一条轨道圈内的轨道控制次数的近圆轨道平面内参数控制方法,达到了相对双脉冲变轨可以大幅缩短整个控制周期的目的。     

地月高能共振循环轨道的快速计算及最优选择

针对现有高能共振循环轨道计算方法存在计算量大、有可能改变轨道共振特性和不能构造共振比大于2.3的地月循环轨道等缺点,本文提出了一种地月圆型限制性三体问题下高能共振循环轨道的快速计算方法.首先根据轨道在月球附近的组成弧段对高能共振循环轨道进行分类;然后根据轨道类型构建二体开普勒椭圆轨道;再进一步计算圆型限制性三体问题下的...     

大规模星座近圆无奇异同步快速轨道预报方法

针对大规模星座轨道预报存在卫星数量多、摄动方程强非线性等难题，提出一种基于平均速率矩阵的多星同步快速轨道预报算法。该算法首先基于哈密顿力学理论建立了二阶带谐项摄动下的轨道动力学模型，其次，利用无奇异轨道根数提出了一种近圆无奇异解析轨道预报模型，并基于Fourier-Bessel级数理论消除真近点角使模型只含有平近点角，简化预报计算过程，在此基础上，基于矩阵理论构造了多星轨道同步预报算法，实现多星轨道同步快速预报。以“星链”卫星星座为例进行仿真，结果表明：提出的方法能够将计算速度提高一个数量级，7天的轨道预报误差小于2.7 km。     

航天器相对运动建模及周期性相对运动求解

面向航天器编队飞行的需求,对椭圆参考轨道航天器非线性周期相对运动条件进行研究,提出了确定椭圆参考轨道编队航天器非线性周期性相对运动条件的新方法。首先,考虑非线性、椭圆轨道等因素,通过哈密尔顿-雅可比(HJ)方程和正则摄动理论,推导了在任意非线性摄动下相对运动的模型和获得不需消耗任何燃料的周期性相对运动轨道的条件;然后,采用时域配点法,结合改进的列文伯格-马夸尔特(LM)法对周期性相对运动的初值进行求解;最后,设计数值仿真算例,利用上述条件,得到不消耗任何燃料的周期性绕飞轨道,由此验证了本文所提模型和方法的正确性。     

Halo orbits in the vicinity of the L 2 libration point in the Sun-Earth system

Methods are proposed for constructing the orbits of spacecraft remaining for long periods of time in the vicinity of the L ₂ libration point in the Sun-Earth system (so-called halo orbits), and the trajectories of uncontrolled flights from low near-Earth orbits to halo orbits. Halo orbits and flight trajectories are constructed in two stages: A suitable solution to a circular restricted three-body problem is first constructed and then transformed into the solution for a restricted four-body problem in view of the real motions of the Sun, Earth, and Moon. For a halo orbit, its prototype in the first stage is a combination of a periodic Lyapunov solution in the vicinity of the L ₂ point and lying in the plane of large-body motion, with the solution for the linear second-order system describing small deviations of the spacecraft from this plane along the periodic solution. The desired orbit is found as the solution to the three-body problem best approximating the prototype in the mean square. The constructed orbit serves as a similar prototype in the second stage. In both stages, the approximating solution is constructed by continuation along a parameter that is the length of the approximation interval. Flight trajectories are constructed in a similar manner. The prototype orbit in the first stage is a combination of a solution lying in the plane of large-body motion and a solution for a linear second-order system describing small deviations of the spacecraft from this plane. The planar solution begins near the Earth and over time tends toward the Lyapunov solution existing in the vicinity of the L ₂ point. The initial conditions of both prototypes and the approximating solutions correspond to the spacecraft’s departure from a low near-Earth orbit at a given distance, perigee, and inclination.     

地月低能轨道转移的混沌控制方法

针对航天器在混沌区域的滑行时间过长，提出一种低能地月轨道转移的混沌控制方法。首先通过地月圆形限制性三体问题(CRTBP)的庞加莱截面图，将混沌区域进行分层并分析其规律，再利用混沌轨道对初始状态高度敏感的特性，在尽可能减少运送时间的前提下实现地月低能轨道转移。该方法的优点是利用混沌区域的固有规律，不需要依靠周期轨道特性。仿真结果表明，本文提出方法仅需施加2~4次脉冲，明显缩短混沌区域的滑行时间，从而实现地月低能转移。     

非线性条件下编队卫星周期性相对运动条件

利用编队卫星机械能守恒原理，提出了非线性条件下求解编队卫星周期性相对运动条件的新方法，给出了非线性周期相对运动的初始条件。编队卫星相对距离较近时，利用非线性周期运动条件，可修正Hill方程的初始条件，抑制编队卫星的长期漂移。编队卫星相对距离较大，非线性因素不可忽略时，利用非线性周期运动条件，可找到不需消耗任何燃料的周期性相对运动轨道。最后的数值仿真结果验证了该方法的正确性。     

Inter-orbital low-thrust transfers in an arbitrary field of forces

Low-thrust transfers between preset orbits are considered in the presence of perturbations of different origin. A simple method of finding the transfer trajectory is suggested, based on linearization of motion near reference orbits. The required accuracy of calculations is achieved by way of increasing the number of reference orbits. The method can also be used in the case of a large number of revolutions around the attracting center: no averaging of motion is required in this case. The suggested method is applicable as well, when the final orbit is specified partially and when there are constraints on the thrust direction. The optimal solution to the linearized problem is not optimal for the original problem; closeness of solutions to these two problems is estimated using a numerical example. Capabilities of the method are also illustrated by examples.     

Method of continuation for optimization of interplanetary low-thrust trajectories

The problem of local optimization of interplanetary low-thrust trajectories is considered with the use of the maximum principle and continuation numerical methods. Two types of problems are analyzed: problems with limited power and problems with limited thrust. The latter problem is generalized by introducing the dependence of thrust and specific impulse on available electric power. In order to reduce the problem of optimal control to a boundary value problem, the Pontryagin maximum principle is used, and then, using the continuation method, this boundary value problem is reduced to the Cauchy problem. Variants of the continuation method for optimizing low-thrust trajectories are presented in the paper, including a new method of continuation for the limited thrust problem, which does not require any choice of the initial approximation for boundary values of conjugate variables.     

A vector method for synthesis of orbits and the structure of satellite constellations for multiswath periodic coverage of the Earth

Single satellites and multisatellite constellations for the periodic coverage of the Earth are considered. The main feature is the use of several cameras with different swath widths. A vector method is proposed which makes it possible to find orbits minimizing the periodicities of coverage of a given area of Earth uniformly for all swaths. Their number is not limited, but the relative dimensions should satisfy the Fibonacci series or some new numerical sequences. The results apply to constellations of any number of satellites. Formulas were derived for calculating their structure, i.e., relative position in the constellation. Examples of orbits and the structure of constellations for the Earth’s multiswath coverage are presented.     

An attitude control approach for compensation of satellite drift in elliptic synchronous orbits

This paper explores the possibility of developing a new attitude control method for satellites in elliptic, 24-hour orbits, in order to compensate for the effect of longitudinal periodic drift relative to the ground station. A simple solar attitude control technique has been proposed for achieving the fixed apparent satellite orientation with respect to the ground segment of the space mission. The proposed control approach appears to be quite attractive for various satellite applications as it can substantially overcome the problems created by the continual periodic angular drift as well as undesirable pitching excitation in the elliptic orbits. Generalizing the analytically developed open-loop control policy results in a significant improvement of the controller performance.     

Single-impulse transfers from orbits of artificial satellites to orbits around <Emphasis Type="Italic">L</Emphasis><Subscript>1</Subscript> or <Emphasis Type="Italic">L</Emphasis><Subscript>2</Subscript> libration points

In the context of the restricted circular three-body problem a method for constructing families of periodic orbits is described. Each orbit contains a segment of transfer from artificial satellite orbit of a smaller body to an orbit around L ₁ or L ₂ points of the Sun-Earth and Earth-Moon systems, a segment of multiple flyby of this libration point, and a segment of return to the artificial satellite orbit. Dependences of velocities at the pericenter on the pericenter radius are given.     

Design of transfer trajectories between resonant orbits in the Earth–Moon restricted problem

The application of dynamical systems techniques to mission design has demonstrated that employing invariant manifolds and resonant flybys enables previously unknown trajectory options and potentially reduces the ΔV$\mathrm{\Delta }V$ requirements. In this investigation, planar and three-dimensional resonant orbits are analyzed and cataloged in the Earth–Moon system and the associated invariant manifold structures are computed and visualized with the aid of higher-dimensional Poincaré maps. The relationship between the manifold trajectories associated with multiple resonant orbits is explored through the maps with the objective of constructing resonant transfer arcs. As a result, planar and three-dimensional homoclinic- and heteroclinic-type trajectories between unstable periodic resonant orbits are identified in the Earth–Moon system. To further illustrate the applicability of 2D and 3D resonant orbits in preliminary trajectory design, planar transfers to the vicinity of L₅ and an out-of-plane transfer to a 3D periodic orbit, one that tours the entire Earth–Moon system, are constructed. The design process exploits the invariant manifolds associated with orbits in resonance with the Moon as transfer mechanisms.