Normal modes are intimately related to the quadratic approximation of a potential at its hyperbolic equilibria. Here we extend the notion to the case where the Taylor expansion for the potential at a critical point starts with higher order terms, and show that such an extension shares some of the properties of standard normal modes. Some symmetric examples are considered in detail.
Higher order normal modes / G. Gaeta, S. Walcher. - In: JOURNAL OF GEOMETRIC MECHANICS. - ISSN 1941-4889. - 12:3(2020 Sep), pp. 421-434. [10.3934/jgm.2020026]
Higher order normal modes
Gaeta G.;
2020-09
Abstract
Normal modes are intimately related to the quadratic approximation of a potential at its hyperbolic equilibria. Here we extend the notion to the case where the Taylor expansion for the potential at a critical point starts with higher order terms, and show that such an extension shares some of the properties of standard normal modes. Some symmetric examples are considered in detail.
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