具L2有界不确定性扰动系统最优跟踪问题的时域解

本文对Ｌ２有界不确定性扰动下的一性系统在时域提出Ｍａｘｍｉｎ最优跟踪问题，给出了问题的时域状态反馈解，这一问题与相应的Ｈ∞问题具有某种一致性，因此，问题的求解方法可为解决领域不确定系统的Ｈ∞最优跟踪问题提供一种时域途径。     

深空探测器定位在共线平动点附近的线性策略

深空探测器需要定位在日-地(月)系的共线平动点L1或L2附近执行探测任务,但由于共线平动点的不稳定性,必须在运行期间进行轨控。对于条件周期轨道(如晕轨道)必须在控制过程中考虑高次项,控制条件复杂,技术上实现相对困难。而某些探测任务,探测器定位在共线平动点附近的条件拟周期轨道(对应L issajous轨道)上亦可以。这种类型的轨道可以离共线平动点较近,那么只需要在控制过程中考虑线性项即可,控制条件简单。以圆型限制性三体问题作为基本模型,采用预估-校正法逼近线性化模型下的目标轨道,给出在轨运行期间的轨控策略亦是可取的,这种控制措施相对而言较简单,容易实现。仿真计算结果表明是可行的,能够提供较高的位置精度。     

深空探测器运行轨道的基本性态

要成功地发射一个深空探测器进入目标轨道,相应的运行过程基本上涉及3个阶段:近地停泊轨道运行段、转移轨道的过渡段和进入目标天体的绕飞段。它们各自的运行状态和相应的数学模型有所差别,特别是转移轨道段的运行特征与绕飞段的卫星轨道的典型特征之间的重大差别,在深空探测任务中受到广泛的重视,如平动点利用中的晕(Halo)轨道和引力加速的节能过渡等。然而,就太阳系而言,这些不同轨道之间有一共同的基本性态,那就是都可以用在牛顿万有引力定律制约下的开普勒轨道(或变化的开普勒轨道)来刻画。本文将针对上述不同运行段轨道对应的数学模型、研究方法和结果,结合我们所做的工作进行综述。     

WSO／UV（世界空间紫外天文台）的轨道特征与轨道保持

WSOO／UV(世界空间紫外天文台)需要发射到日-地(月)系的共线平动点L1附近进行巡天观测，相对日-地(月)要求其几何位置几乎不变，因此有必要阐明共线平动点的动力学特征及其附近的运动状况。本文基于这一点，对限制性三体模型下，日-地(月)系中共线平动点附近扰动运动的稳定性作了理论分析，给出了WSO／UV轨道保持的条件及其在运行阶段的轨控措施。     

关于拟线性椭圆型方程在广义Sobolev空间中解的正则性

本文讨论了下面方程Ｄｉｒｉｃｈｌｅｔ问题在广义Ｓｏｂｏｌｅｖ空间中解中的正则性－ｄ／ｄｘ１ａ１（ｘ，ｕ，Ｄｕ）＋ａ（ｘ，ｕ，Ｄｕ）＝０，ｘ∈Ω其中Ω∈Ｒ是有界区域，证明了上述问题在Ｗ（Ω）和Ｗ（Ω）在存在有界广义解。     

透视仿射对应在画法几何相交问题中的应用

论述了透视仿射对应理论及该理论在解决工程实际问题方面的应用，并举例论述了，透视仿射对应理论在画法几何的相交问题中的应用。为工程技术人员图解相交问题中的交点、交线提供了一种新的方法。     

Alternative transfer to the Earth–Moon Lagrangian points L4 and L5 using lunar gravity assist

Lagrangian points L4 and L5 lie at 60° ahead of and behind the Moon in its orbit with respect to the Earth. Each one of them is a third point of an equilateral triangle with the base of the line defined by those two bodies. These Lagrangian points are stable for the Earth–Moon mass ratio. As so, these Lagrangian points represent remarkable positions to host astronomical observatories or space stations. However, this same distance characteristic may be a challenge for periodic servicing mission. This paper studies elliptic trajectories from an Earth circular parking orbit to reach the Moon’s sphere of influence and apply a swing-by maneuver in order to re-direct the path of a spacecraft to a vicinity of the Lagrangian points L4 and L5. Once the geocentric transfer orbit and the initial impulsive thrust have been determined, the goal is to establish the angle at which the geocentric trajectory crosses the lunar sphere of influence in such a way that when the spacecraft leaves the Moon’s gravitational field, its trajectory and velocity with respect to the Earth change in order to the spacecraft arrives at L4 and L5. In this work, the planar Circular Restricted Three Body Problem approximation is used and in order to avoid solving a two boundary problem, the patched-conic approximation is considered.     

Two-manoeuvres transfers between LEOs and Lissajous orbits in the Earth–Moon system

The purpose of this work is to compute transfer trajectories from a given Low Earth Orbit (LEO) to a nominal Lissajous quasi-periodic orbit either around the point L₁ or the point L₂ in the Earth–Moon system. This is achieved by adopting the Circular Restricted Three-Body Problem (CR3BP) as force model and applying the tools of Dynamical Systems Theory.     

航天器分裂体或抛射物的轨道形成和演化

由卫星和碎片爆炸或相互间碰撞所产生的分裂体,或由在轨航天器向外抛射所产生的抛射物,对空间环境的影响正日益增大。对它们轨道形成和演化的研究可以为分析空间解体事件提供一种有效方法。本文利用Kep-ler运动积分以及受摄二体问题的分析解,建立了分裂体或抛射物的轨道形成及其演化与分裂或抛射速度之间的关系,从而为理解以各个方向、不同大小的速度分裂或抛射的物体的轨道演化特征提供理论依据。文章最后通过数值验证表明了该方法的有效性。     

Framing holes within a loop hierarchy

We investigate the relation between nontrivial spatial concepts such as holes and string loops from a qualitative spatial reasoning perspective. In particular, we concentrate on a family of puzzles dealing with this kind of objects and explain how a loop formed in a string shows a similar behavior to a hole in an object, at least regarding the qualitative constraints it imposes on the solution of the puzzle. Unlike regular holes, however, we describe how string loops can be dynamically created and destroyed depending on the actions on the string. Furthermore, under a Knowledge Representation point of view, we provide a formalization that allows the different puzzle states to be described in terms of string crossings and loops, together with the actions that can be executed for a state transition and the complex effects they cause on the state representation. This implies the consideration of a formal representation of the side effects of actions that create or destroy string loops and the soundness of this representation with respect to the more general representation of string states in knot theory.