Spacecraft Formation Dynamics and Design
Spacecraft Formation Dynamics and Design
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DOI：
10.2514/1.13002
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发表时间：
2004-08
影响因子：
2.6
通讯作者：
V. Guibout;D. Scheeres
中科院分区：
文献类型：
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作者：
V. Guibout;D. Scheeres
两点边值问题解的研究已应用于航天器编队动力学和设计中。其基本思想是将航天器编队的运动建模为参考解附近的哈密顿动力学系统。然后，可以使用通过求解汉密尔顿-雅可比方程得到的生成函数来解析地描述非线性相流。这样的方法是非常强大的，并允许任何哈密顿动力系统的研究独立于其向量场的复杂性和任何两点边值问题的解决方案，仅使用简单的功能评估来解决。该方法的细节是通过一个非平凡的例子，在地球轨道上的编队设计的研究。在分析中，考虑了J2和J3重力系数的影响。参考轨道选择为具有高倾角i = π/3和偏心率e = 0.3的轨道。考虑了两个任务。首先，在一个月的时间内，将多个任务建模为给定时刻的构型，找到以最小的燃料消耗完成任务的最优构型序列;然后，利用该理论找到稳定构型，使得航天器在有限的时间内相互靠近。这两个任务都是非常困难的使用传统的方法，但很容易解决与所提出的方法。
Previous research on the solutions of two-point boundary value problems is applied to spacecraft formation dynamics and design. The underlying idea is to model the motion of a spacecraft formation as a Hamiltonian dynamic system in the vicinity of a reference solution. Then the nonlinear phase flow can be analytically described using generating functions found by solving the Hamilton‐Jacobi equation. Such an approach is very powerful and allows the study of any Hamiltonian dynamical systems independent of the complexity of its vector field and the solution of any two-point boundary value problem to be solved using only simple function evaluations. The details of the approach are presented through the study of a nontrivial example, the design of a formation in Earth orbit. For the analysis, the effect of the J2 and J3 gravity coefficients are taken into account. The reference trajectory is chosen to be an orbit with high inclination, i = π/3, and eccentricity, e = 0.3. Two missions are considered. First, given several tasks over a one-month period modeled as configurations at given times, the optimal sequence of reconfigurations to achieve these tasks with minimum fuel expenditure is found. Next, the theory is used to find stable configurations such that the spacecraft stay close to each other for an arbitrary but finite period of time. Both of these tasks are extremely difficult using conventional approaches, yet are simple to solve with the presented approach.