Symmetries of line bundles and Noether theorem for time-dependent nonholonomic systems

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doi:10.3934/jgm.2018006

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2018, Volume 10, Issue 2: 173-187. Doi: 10.3934/jgm.2018006

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Symmetries of line bundles and Noether theorem for time-dependent nonholonomic systems

Mathematical Institute SANU, Serbian Academy of Sciences and Arts, Kneza Mihaila 36, 11000 Belgrade, Serbia

Received: August 31, 2016

Revised: February 28, 2018

Published: May 2018

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Abstract

We consider Noether symmetries of the equations defined by the sections of characteristic line bundles of nondegenerate 1-forms and of the associated perturbed systems. It appears that this framework can be used for time-dependent systems with constraints and nonconservative forces, allowing a quite simple and transparent formulation of the momentum equation and the Noether theorem in their general forms.

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Mathematics Subject Classification: Primary: 37J15, 37J60, 70F25; Secondary: 70H25, 70H33.

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