Explicit methods to generate new canonical sets of elements are presented, together with an analysis on the structure of existing canonical elements that are used in the study of the perturbed two-body problem. New non-singular sets of canonical elements are introduced. Among these sets, the resonant canonical variables are non-singular for circular orbits and display an action-angle-like behaviour for the unperturbed Kepler problem, if their associated generalized frequency is tuned to match the conserved energy. They also prove to be an efficient tool for both qualitative and quantitative studies of perturbations.

中文翻译：

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通过显式规范变换和共振规范变量进行哈密顿量约简

提出了生成新规范元素集的显式方法，并对用于研究摄动二体问题的现有规范元素的结构进行了分析。引入了新的非奇异规范元素集。在这些集合中，共振正则变量对于圆形轨道来说是非奇异的，并且如果将它们相关的广义频率调整为与守恒能量相匹配，则对于未受扰动的开普勒问题表现出类似作用角的行为。它们还被证明是定性和定量研究扰动的有效工具。