This paper discusses the theory of oscillatory normal modes, and its extension to general multi-body mechanical systems. We first review the efforts to generalize modal analysis to the non-linear case. This body of knowledge is vast and spread across several subfields of mathematics, physics, and engineering. We concisely summarize these results, and connect them together using a language familiar to the control theorist. We then propose a direct way of extending nonlinear modes to mechanical systems with a non Euclidean metrics (e.g. robots).

中文翻译：

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保守机械系统中的非线性模式综述

本文讨论了振荡法线模的理论，并将其扩展到一般的多体力学系统。我们首先回顾一下将模态分析推广到非线性情况的工作。这套知识是巨大的，分布在数学，物理学和工程学的几个子领域。我们简要总结了这些结果，并使用控制理论家熟悉的语言将它们连接在一起。然后，我们提出了一种将非线性模式扩展到具有非欧几里得度量标准的机械系统的直接方法（例如，机器人）。