水星环绕轨道动力学与控制研究

发布时间：2018-10-20 10:11

【摘要】：水星探测对研究太阳系演化和生命起源具有重要意义。水星是太阳系最内侧的行星，其公转轨道有着不可忽略的偏心率，这就导致环绕水星的航天器会受到周期时变的太阳引力影响。本文特别针对这种轨道动力学环境，对水星环绕轨道的轨道动力学和轨道保持控制等问题进行研究。当航天器在水星影响球内运行时，本文考虑了来自太阳的椭圆第三体摄动以及水星非球形摄动中的J2，J3项，对环绕轨道的动力学环境进行建模。为研究轨道根数的长期变化趋势，本文采用了Lie变换的方法对水星环绕轨道进行双平均化。平均化后系统降为单自由度系统，此时哈密顿正则方程的平动点即为通常意义上的冻结轨道。本文探讨了航天器偏离目标冻结轨道的轨道修正问题，在二体模型中针对同一轨道上的不同e相点，设计了转移至新的目标冻结轨道的轨道转移方案，分析了不同相点上向冻结轨道进行轨道转移的可行性和能量消耗，而后将轨道转移方案在摄动条件下加以修正。冻结轨道的存在条件有限，不一定能够满足实际任务的约束。因此，，本文提出了一种基于平均化模型和参数优化的连续小推力控制律，通过连续推力调节每种摄动的大小以使其符合冻结轨道的存在条件，实现水星环绕轨道的人工冻结。本文选取了与每项摄动相关的伪摄动参数作为待优化参数，并推导了人工冻结轨道的冻结条件及约束方程，搜寻最优的伪摄动参数，以使轨控效率达到最佳。通过大范围的仿真算例，本文分析了伪摄动参数随相关轨道根数的演化情况，并对本方法的可行性进行评估。最后，本文研究了环绕水星的高轨准周期轨道。这类轨道的尺寸极大且不具有严格意义上的周期性，有些轨道大大超出水星影响球半径的大小。为此，本文将在太阳-水星系统所对应的椭圆限制性三体问题下对高轨准周期轨道进行探讨。本文根据水星动力学环境和航天任务需求，定义了水星高轨准周期轨道，利用同伦法从圆限制性三体问题中的逆行和顺行周期轨道族出发，逐渐提高椭圆限制性三体系统中的偏心率，最终求得太阳-水星系统中的高轨准周期轨道。最后，本文研究了这类准周期轨道较长期运行的稳定性。
[Abstract]:Mercury exploration is of great significance in studying the evolution of the solar system and the origin of life. Mercury is the innermost planet in the solar system, and its orbit has an unnegligible eccentricity, which causes the spacecraft orbiting Mercury to be influenced by the periodic time-varying solar gravity. In this paper, the orbit dynamics and orbit retention control of Mercury orbit are studied especially in this orbit dynamic environment. When the spacecraft is operating in the sphere of influence of Mercury, the elliptical third body perturbation from the sun and the J _ 2N _ J _ 3 term in the non-spherical perturbation of Mercury are considered in this paper, and the dynamic environment around the orbit is modeled. In order to study the long-term variation trend of orbital root number, the Lie transform is used to double average the orbit around Mercury. When the system is reduced to a single degree of freedom system after averaging, the translational point of the Hamiltonian canonical equation is the frozen orbit in the usual sense. In this paper, the orbit correction problem of spacecraft deviating from the frozen orbit of the target is discussed. For different e phase points in the same orbit in the two-body model, an orbit transfer scheme is designed to transfer to the new frozen orbit of the target. The feasibility and energy consumption of orbit transfer to frozen orbit at different phase points are analyzed, and then the orbital transfer scheme is modified under perturbation condition. The existence condition of frozen orbit is limited, which can not satisfy the constraint of actual task. Therefore, this paper presents a continuous small thrust control law based on averaging model and parameter optimization, which adjusts the size of each perturbation through continuous thrust to make it conform to the existence condition of frozen orbit, and realizes the artificial freezing of Mercury orbit. In this paper, the pseudo-perturbation parameters associated with each perturbation are selected as the parameters to be optimized, and the freezing conditions and constraint equations of the artificial frozen orbit are derived, and the optimal pseudo-perturbation parameters are searched for the optimal orbit control efficiency. In this paper, the evolution of pseudo-perturbation parameters with the root number of related orbits is analyzed by a large range of simulation examples, and the feasibility of this method is evaluated. Finally, the high-orbit quasi-periodic orbit around Mercury is studied. These orbits are large in size and do not have a strict periodicity, and some orbits far exceed the radius of the sphere affected by Mercury. Therefore, in this paper, the quasi-periodic orbit of high orbit is discussed under the elliptic restricted three-body problem corresponding to the sun-Mercury system. According to the dynamic environment of Mercury and the requirements of space mission, the quasi-periodic orbit of Mercury in high orbit is defined in this paper. The homotopy method is used to start from the family of retrograde and anteroposterior periodic orbits in the circular restricted three-body problem. The eccentricity of elliptical restricted three-body system is gradually increased, and the quasi-periodic orbit of high orbit in the Sun-Mercury system is finally obtained. Finally, the stability of this kind of quasi-periodic orbit is studied.
【学位授予单位】：清华大学
【学位级别】：博士
【学位授予年份】：2013
【分类号】：P173

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