State Transition Matrices for Terminal Rendezvous Studies: Brief Survey and New Example
State Transition Matrices for Terminal Rendezvous Studies: Brief Survey and New Example
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DOI：
10.2514/2.4211
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发表时间：
1998
影响因子：
2.6
通讯作者：
T. Carter
中科院分区：
文献类型：
--
作者：
T. Carter
对大部分已发表的关于线性化交会的资料进行了简要的综述和分类。在此基础上，提出了一种适用于一般中心力场的终端交会问题的新解。利用该解和相关伴随系统的解构造一般状态转移矩阵。由于假设的通用性，这个状态转移矩阵非常简洁和灵活。最后，利用Tschauner - Hempel方程，将本文的工作应用于牛顿引力场中任意开普勒轨道附近的终端交会问题。由于此解决方案是根据真正的异常提出的，因此需要相当小心地避免这类问题中典型的奇点类型。结果是线性化交会研究的状态转移矩阵，被认为比文献中发现的其他版本更简单，更方便。线性化的运动方程在描述任务的最终交会阶段或卫星站保持时是有用的。天体动力学的这些领域有丰富的线性化方法可供研究人员使用，以及由此产生的数学分析和计算。本文简要介绍了在交会研究中发现的线性模型的类型，然后是一个新的一般模型，它包含了许多以前的工作作为特殊情况。这项工作结合了19世纪天体力学的一些思想和最近的一些发现。由于这个新模型假设一个一般的中心力引力场，在设计相对简单的状态过渡矩阵时，避免了许多建立在特定情况下的复杂性，从而适用于各种问题。然后利用Tschauner - Hempel方程将工作应用于引力场中线性化交会的重要特殊情况，该情况需要平方反比定律。事实上，正是这个问题激发了这项研究。寻找一个没有奇点的解，对任何开普勒轨道都有效，避免通用函数，可能导致一组混乱的方程。新的通用模型避免了这种混乱，并以相对简洁的形式呈现结果。
Abriefsurvey and classie cation of much of the published material on linearized rendezvous is presented. Thisis followed by a new form of solution of the terminal rendezvous problem that is valid in a general central force e eld. This solution and the solution of the related adjoint system are used to construct a general state transition matrix. Because of the generality of the assumptions, this state transition matrix is very concise and e exible. Finally, the work is applied to the problem of terminal rendezvous near any Keplerian orbit in a Newtonian gravitational e eld using the Tschauner ‐Hempel equations. Because this solution is presented in terms of the true anomaly, considerable care is taken to avoid the types of singularities that are typical in this kind of problem. The result is a state-transition matrix for linearized rendezvous studies that is thought to be simpler and more convenient than other versions found in the literature. I. Introduction L INEARIZED equations of motion are useful in describing the terminal rendezvous phase of a mission or in satellite station keeping. These areas of astrodynamics are rich in the variety of linearizations available to investigators and in the resulting mathematical analysis and computations that follow. This paper presents a brief survey of the types of linear models found in rendezvous studies, followed by a new general model that incorporates much previous work as special cases. The work combines some ideas in 19th century celestial mechanics with some recent discoveries. Because this new model assumes a general central force gravitational e eld,muchofthecomplexitiesfoundinspecie ccasesareavoidedin designingarelativelysimplestatetransitionmatrixthatisapplicable to a variety of problems. The work is then applied to the important special case of linearized rendezvous in a gravitational e eld dee ned by an inverse square law using the Tschauner ‐Hempel equations. In fact, it was this problem that motivated the study. The search for a solution devoid of singularities, valid for any Keplerian orbit, that avoids universal functions can lead to a cluttered set of equations. The new general model avoids much of this clutter and presents the results in a relatively concise form.