Some observations are made on coordinate selection for the two most fundamental problems of astrodynamics, namely orbit dynamics and attitude dynamics, and some interesting connections and analogies between the two problems are explored. While an infinity of coordinate choices are feasible for each of these problems, we review four coordinate choices for each problem, including several that lead to governing differential equations that are regular, and in some cases, rigorously linear. Some methodology is introduced that has a universal flavor with implications for dynamical systems broadly. We show how dramatic qualitative and quantitative alteration of the mathematical description of the motion can be accomplished by introduction of redundant coordinates to describe the evolution of the dynamics in a higher dimensioned space. Some observations are made on an analogy between the two central problems of interest. One of the regularizing transformations studied for orbital dynamics is motivated directly by this analogy. Finally broadly applicable analytical and computational developments are presented that provide a measure of nonlinearity over a worst-case region of state space in the vicinity of a reference trajectory; this measure is used to evaluate the several coordinate choices.

中文翻译：

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它有多非线性？轨道与姿态动力学非线性教程

对航天动力学的两个最基本的问题，即轨道动力学和姿态动力学，进行了坐标选择的观察，并探讨了这两个问题之间的一些有趣的联系和类比。尽管对于这些问题中的每一个问题，无穷大的坐标选择都是可行的，但是我们为每个问题回顾了四个坐标选择，其中包括导致规则微分方程（在某些情况下是严格线性的）的一些控制问题。引入了一些具有普遍风味的方法，广泛地影响了动力学系统。我们展示了如何通过引入冗余坐标来描述运动的数学描述中的戏剧性的定性和定量改变，以描述更高维度空间中动力学的演变。对两个感兴趣的中心问题之间的类比做了一些观察。这个类比直接推动了针对轨道动力学研究的正则化变换之一。最后，提出了广泛适用的分析和计算发展，这些发展提供了在参考轨迹附近状态空间的最坏情况区域上的非线性度量。此度量用于评估多个坐标选择。