Close relative motion on distant retrograde orbits

Distant Retrograde Orbits (DROs) in the Earth-Moon system have great potential to support varieties of missions due to the favorable stability and orbital positions. Thus, the close relative motion on DROs should be analyzed to design formations to assist or extend the DRO missions. However, as the reference DROs are obtained through numerical methods, the close relative motions on DROs are non-analytical, which severely limits the design of relative trajectories. In this paper, a novel approach is proposed to construct the analytical solution of bounded close relative motion on DROs. The linear dynamics of relative motion on DRO is established at first. The preliminary forms of the general solutions are obtained based on the Floquet theory. And the general solutions are classified as different modes depending on their periodic components. A new parameterization is applied to each mode, which allows us to explore the geometries of quasi-periodic modes in detail. In each mode, the solutions are integrated as a uniform expression and their periodic components are expanded as truncated Fourier series. In this way, the analytical bounded relative motion on DRO is obtained. Based on the analytical expression, the characteristics of different modes are comprehensively analyzed. The natural periodic mode is always located on the single side of the target spacecraft on DRO and is appropriate to be the parking orbits of the rendezvous and docking. On the basis of quasi-periodic modes, quasi-elliptical fly-around relative trajectories are designed with the assistance of only two impulses per period. The fly-around formation can support observations to targets on DRO from multiple viewing angles. And the fly-around formation is validated in a more practical ephemeris model.     

Aerial-ground collaborative routing with time constraints

The advancement of autonomous technology makes electric-powered drones an excellent choice for flexible logistics services at the last mile delivery stage. To reach a balance between green transportation and competitive edge, the collaborative routing of drones in the air and trucks on the ground is increasingly invested in the next generation of delivery, where it is particularly reasonable to consider customer time windows and time-dependent travel times as two typical time-related factors in daily services. In this paper, we propose the Vehicle Routing Problem with Drones under Time constraints (VRPD-T) and focus on the time constraints involved in realistic scenarios during the delivery. A mixed-integer linear programming model has been developed to minimize the total delivery completion time. Furthermore, to overcome the limitations of standard solvers in handling large-scale complex issues, a space-time hybrid heuristic-based algorithm has been developed to effectively identify a high-quality solution. The numerical results produced from randomly generated instances demonstrate the effectiveness of the proposed algorithm.     

Parameterized design of abort trajectories with a lunar flyby for a crewed mission

This article proposes an analytical preliminary design method for abort trajectory with a lunar flyby and the trajectory ergodic representation based on parameterization, as well as their application in studying the abort trajectories’ characteristics. First, by introducing two parameters, the perilune altitude and the perilune transfer time, the preliminary solution is developed parametrically using pseudostate theory to connect two special Lambert processes. The fast convergence of the improved differential correction under the high-fidelity gravity field verifies the accuracy of the proposed preliminary design method. Next, the two parameters are regarded as a set of variables to define an abort trajectory. Based on this, an ergodic representation of the abort trajectory with a certain abort time is yielded using the proposed design method, which offers a global view of the feasible abort trajectories. In addition, the influences of some factors on the performance of these abort trajectories are investigated based on the proposed design method and ergodic representation. The simulation results show that the abort time and the transfer time of the nominal trajectory significantly affect the ergodic representation and characteristics of the abort trajectory.     

Four-body cislunar quasi-periodic orbits and their application to ballistic lunar transfer design

Examining the properties of quasi-periodic orbits provides insight into the Sun-perturbed environment in cislunar space. In this investigation, quasi-periodic trajectories and their properties are explored in the Sun-Earth-Moon four-body problem. Computation and the stability characteristics of families of invariant tori are detailed. Furthermore, this investigation offers a framework for construction of ballistic lunar transfer trajectories in the four-body problem. The framework leverages manifold trajectories to supply a set of initial conditions for construction of periapsis Poincaré maps. Periapsis maps reduce the dimensionality of the space and illuminate solutions of interest as a basis to produce feasible families of transfers. Through a continuation process, families of ballistic transfers and families of transfers that include powered lunar flybys are constructed. Ultimately, these solutions supply an initial guess for transition to the Sun-Earth-Moon ephemeris model.     

一阶微分方程终值问题拟解的存在性

利用拟上下解方法,研究了一阶微分方程终值问题u′(t)=f()t,u(t),u(T)=xT拟解的存在性,并通过构造单调迭代序列得到该终值问题的最大最小拟解。     

基于贪婪算法的航空存储资源共享机制研究

航空存储网格存储服务是汇聚航空高性能计算中心、各个组织服务器以及单个PC机贡献的存储资源,按照一定规则为用户提供数据存储的注册、分配、调度、释放的共享资源的三级存储架构。在此条件下的资源共享问题属于NP完全问题。为此,我们提出启发式贪婪算法,并对系统性能进行仿真,得出用户请求与负载关系。     

基于线性位移模式的环形谐振子理论研究

环形谐振子理论是谐振陀螺研究领域的重要内容,然而在目前经典环形谐振子理论中,仍 存在很多问题尚未解决,例如:挠度控制方程不能精确求解环形结构的弯曲问题,获得的二阶弯曲 角频率及进动系数理论解不能充分反映出其随尺寸参数(如高度h、曲率半径r 等)变化的影响规 律等。为了克服上述不足,从环形结构理论的基本假设和基本条件出发,基于环形结构的线性位 移模式假设、虚功原理和哈密顿原理,建立新的环形谐振子理论,包括广义本构关系、平衡方程和 边界条件等,获得环形结构静态弯曲问题的解析求解方法和动态问题的理论解。最后,针对典型 的环形结构静、动态问题,通过与其他理论结果进行对比,验证了理论和求解方法的正确性。工作 表明,进动系数不是恒定的,其值会随着结构尺寸的不同在0.4附近很小范围内发生变化。