Method of virtual trajectories for the design of gravity assisted missions

A novel method of virtual trajectories is proposed for the design of multiple gravity assist trajectories. The database of virtual trajectories can be tabulated for any planetary sequence and used in subsequent calculations. Requirements for the mission duration and the launch date are taken into account during the iterative procedure of database screening and refinement. The results of applying the virtual trajectories method to the design of a mission to Uranus are presented.     

Solar Probe Mission with Multiple Gravity-Assist Maneuvers Realized with Conversion Launchers

The trajectories of solar missions that could be realized with conversion launchers are investigated. The insufficient energy resources of the rocket launchers is compensated by multiple gravity-assist maneuvers near terrestrial planets. A method based on the construction of a set of attainability for all the mission trajectories rather than on optimization of separate trajectories is presented, which makes it possible to analyze the problem more widely and to find global extremums using various criteria. Detailed features of the most rational trajectories are given.     

Method of virtual trajectories for the design of gravity assisted missions

A method of virtual trajectories is proposed for the design of multiple gravity assist trajectories. The method comprises two principal stages. First, for a chosen planetary sequence, a database of virtual trajectories is tabulated. Then the database screening and refinement are performed. The design of trajectory to Jupiter is presented.     

Design of Interplanetary Transfers with Passive Gravity Assists and Deep Space Maneuvers

In the paper, the problem of designing interplanetary trajectories with several swing-bys and deep-space maneuvers is solved using the method of virtual trajectories developed by the authors. The algorithms for the calculation of both heliocentric and planetocentric trajectory arcs are presented, including the case of resonant trajectories. The results of applying the method of virtual trajectories to the problem of designing an interplanetary transfer to Jupiter are given and compared with the baseline trajectories for the Juno, Europa Clipper, and Laplace missions.     

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。     

载人机动装置救援轨迹优化设计

本文研究宇航员携带舱外机动装置（ＭＭＵ）进行舱外飞行，营救脱离空间站的目标，随后返回空间站的Ｈｉｌｌ制导方法。根据最小燃料指标，精度要求和时间约束，优化设计ＭＭＵ出舱营救脱离空间站的宇航员或其它装置的飞行轨迹。求出１７种典型情况下的最小燃料解，提出了救援轨迹设计准则。本文分析了ＭＭＵ交会目标过程中，导航和控制误差对Ｈｉｌｌ制导瞄准误差的影响，提出了用多脉冲Ｈｉｌｌ制导按标称最优轨迹飞行的设计方案，     

The use of solutions to problems of spacecraft trajectory optimization in impulse formulation when solving the problems of optimal control of trajectories of a spacecraft with limited thrust engine: II

As examples of application of the technique suggested in the first part of this work, the problems of optimizing the trajectories of spacecraft transfers between circular coplanar orbits are considered in this second part. During the transfer the spacecraft is controlled by the vector of thrust of a limited-thrust jet engine. The mass consumption is minimized for a limited time of transfer. Extreme trajectories with two and three powered sections (Homan-type and bi-elliptic transfer trajectories) are numerically determined. The solution of these well-studied problems allows one to compare the results of applying the suggested technique with the results of application of other previously used techniques.     

Trajectories of in-plane periodic solutions of tethered satellite system projected on van der Pol planes

In this paper, in-plane periodic solutions for a dumbbell model in elliptic orbits are searched using bifurcation, and their trajectories are projected on the van der Pol planes. The trajectories projected on the van der Pol plane will be employed as a tool to predict when the control of delayed feedback control will need to act to maintain the periodic motions.     

Analysis of spatiotemporal trajectories for stops along taxi paths

Stops along taxi trajectories, such as picking up and dropping off passengers, are spatially clustered and related to certain attributes of places where stops are made. To detect the hidden knowledge regarding these places, this article examines the semantics of massive taxi stops in a large city. Each taxi trajectory is modeled as a series of sequential semantic stops labeled by street names. All the trajectories can be examined as a document corpus, from which the hidden themes of the stops are identified through Latent Dirichlet Allocation model. Conventional GIS tools are coupled with topic modeling toolkit to visualize and analyze potential information of stop topics for understanding intra-city dynamics. The effectiveness of this approach is illustrated by a case study using a large dataset of taxi trajectories including approximately 4,000 taxis in Wuhan, China.     

基于分段常滑翔角的长航时纵向远程滑翔飞行方程近似解

提出用包含地球旋转效应的n个常滑翔角飞行段近似实际滑翔飞行轨迹的方法。基于该方法推导了长航时纵向远程滑翔飞行轨迹近似解，并给出了各段常滑翔角、滑翔时间的求解方法及整个滑翔轨迹近似计算步骤。文中算例结果表明，该近似求解方法计算得到的滑翔航程和滑翔时间与实际值相差很小，航程误差率约为0．7％，时间误差率约为0．6％，因此该方法在近似小初始滑翔角的长航时远程纵向滑翔飞行时是有效的、可行的，尤其针对航程在地球半圈以上的滑翔飞行轨迹。     

Optimization of interplanetary trajectories for spacecraft with ideally regulated engines using the continuation method

The problem of optimization of interplanetary trajectories is considered for spacecraft with a small-thrust ideally regulated engine. When the maximum principle is used, determination of the optimal trajectory is reduced to solution of a two-point boundary value problem for a system of ordinary differential equations. In order to solve this boundary value problem, the method of continuation in parameter is used, and with the help of it the formal reduction of the boundary value problem to a Cauchy problem is performed. Different variants of the continuation method are considered, including the method of continuation in the gravitational parameter which allows one to find extreme trajectories with a preset angular distance. The issues of numerical realization of the continuation method are discussed, and numerical examples of its use for solving the problems of optimization of interplanetary trajectories are presented.     

不确定条件下采用协方差描述函数法的再入轨迹鲁棒优化

Uncertainties are taken into account in reentry trajectory optimization and a robust trajectory optimization model is constructed based on the robust optimization theory. There are computational difficulties in solving this robust trajectory optimization problem due to the random variables associated with the uncertainties. To overcome these difficulties, the covariance analysis describing function technique (CADET) is employed to convert the robust trajectory optimization model into an equivalent deterministic trajectory optimization formulation, which is then solvable by using the existing pseudo spectral method. In the case study, a robust reentry trajectory optimization problem considering the uncertainties of aerodynamic parameters is solved to obtain the robust optimal trajectories. By comparing with the traditional deterministic optimal trajectories, the robust optimal trajectories are significantly less sensitive to the uncertainties of aerodynamic parameters, showing the effectiveness of the presented method.      

A Study of a Possible Method of Observing Solar Eclipses from Satellite Orbits

We study a possibility of observing the eclipses of the Sun by the Moon from satellite orbits. The scientific tasks planned to be solved onboard satellites are considered. The requirements for the observation of eclipses and for the appropriate satellite trajectories are formulated. A technique of the analysis and synthesis of such trajectories is developed, and some results of preliminary ballistic studies are presented. These results confirm the efficiency of observing the eclipses onboard satellites.     

飞月轨道引力捕获设计方法研究

利用太阳引力摄动与月球绕飞设计的地月转移轨道（飞月轨道），与霍曼转移相比，虽然飞行时间较长（约三、四个月），但可显著节省速度增量（可达１５０米／秒），对无人月球探测器尤为适合。应用平面圆型限制性四体问题动力学模型，选择从月球出发的初始条件。借助“地心距－时间曲线”，从平面圆型限制性四体问题转换为一般的限制性四体问题。通过典型模拟计算，分析负向积分（从月球轨道出发）初始轨道参数及太阳方位对月球探测器     

亚轨道飞行器能量管理段在线轨迹设计及仿真

对亚轨道飞行器能量管理段在线轨迹生成方案进行了研究。该方案将地面投影几何轨迹参数化,通过迭代计算参数生成标准轨迹,验证轨迹可行性并选择最优轨迹。经仿真验证,该方案能够在较短时间内完成轨迹的在线生成,结果满足进场着陆要求。     

Hill区域内基于推广的Poincaré映射的低能逃逸/捕捉轨道

给出了Hill区域内基于推广的Poincare映射的低能逃逸轨道的计算.文中的推广的Poincare映射需要在相空间中选取两个(而非一个)与流相截的面,即将包含某个天平动点的截面通过轨道来映射到近拱点的通道面上的,在数值上通过总变差减小的Runge-Kutta方法来实现两个相面之间的映射.捕捉轨道则可由Hill三体模型的对称性直接导出.最后,关于Rhea的二维、三维的逃逸和捕捉轨道的仿真结果验证了该方法的精度和鲁棒性.     

A dynamical approach to precision entry in multi-body regimes: Dispersion manifolds

The identification of trajectories that target a precise location and approach vector during planetary entry is sensitive to the quality of the startup arc supplied to iterative path planning and guidance algorithms. These sensitivities are especially evident when multi-body effects are significant; low-energy spacecraft trajectories that dwell near the gravitational boundary of two bodies, for instance, are more susceptible to third-body effects. Dynamical sensitivities are also significant when maneuvers are scheduled within a region of space susceptible to multi-body effects. The present study considers precision entry targeting from the perspective of the multi-body problem.     

Spatial approaches to moons from resonance relative to invariant manifolds

In this study, the final approach to a moon or other body from resonance is explored and compared to the invariant manifolds of unstable periodic orbits. It is shown that the stable manifolds of planar Lyapunov orbits can act as a guide for the periods or resonances that are required for the final approach in both the planar and spatial problems. Previously developed techniques for the planar problem are expanded for use with resonances and used for comparison with trajectories approaching a moon from these resonances. A similar technique is then used for exploring the relationship of invariant manifolds to approach trajectories in the spatial problem. It is shown that the invariant manifolds of unstable periodic orbits provide insight into the trajectory design, and they can be used as a guide to the more direct approach trajectories.     

基于地球引力变轨的日冕探测器轨道设计

研究了相对黄道面有一定倾角的探测器轨道设计的问题。以金星借力轨道设计为例,分析了轨道偏心率与轨道倾角增量之间的关系。根据C3匹配原理搜索了“地球-中间天体-地球”多天体交会的发射窗口。最后,设计了与地球轨道周期相等的三次地球借力轨道,该轨道倾角可以达到黄纬30°以上。理论分析及仿真结果表明:基于地球引力设计此类轨道时,应采用多天体交会方案,才能既保证地球逃逸能量低,又保证首次飞入地球影响球前轨道偏心率较大的双重指标;同时应采用多次地球借力方案,该方案具有每次借力后轨道偏心率逐渐减小的特点,当其减小到零时,再次借力后轨道倾角不会继续增加。