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Acta Mechanica

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05.09.2020 | Original Paper

On the reduction of nonlinear mechanical systems via moving frames: a bead on a rotating wire hoop and a spinning top

verfasst von: C. H. C. C. Basquerotto, A. Ruiz

Erschienen in: Acta Mechanica | Ausgabe 12/2020

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Abstract

The aim of this work is to show how the moving frames method can be applied for reducing and solving two nonlinear mechanical systems: a bead on a rotating wire hoop and a spinning top. Once both problems are adequately formulated, we explicitly determine the corresponding moving frames associated to the symmetry group of transformations admitted by the systems. The knowledge of the moving frames for the action of the corresponding symmetry groups permits to perform order reductions. Furthermore, we are able to compute the general solutions to each problem from the general solutions of the corresponding reduced systems. Finally, we also discuss the connection of the presented approach with the classical method provided by the celebrated Noether’s Theorem.

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Titel: On the reduction of nonlinear mechanical systems via moving frames: a bead on a rotating wire hoop and a spinning top
verfasst von: C. H. C. C. Basquerotto
A. Ruiz
Publikationsdatum: 05.09.2020
Verlag: Springer Vienna
Erschienen in: Acta Mechanica / Ausgabe 12/2020
Print ISSN: 0001-5970
Elektronische ISSN: 1619-6937
DOI: https://doi.org/10.1007/s00707-020-02798-1

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