A review on nonlinear modes in conservative mechanical systems

Abstract

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).