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Acta Mechanica

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10-12-2023 | Original Paper

Noether theorem and its inverse for nonstandard generalized Chaplygin systems

Authors: S. X. Jin, Y. M. Li, X. W. Chen

Published in: Acta Mechanica | Issue 2/2024

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Abstract

In this paper, the Noether theorems and their inverse theorems for generalized Chaplygin systems with two types of nonstandard Lagrangians, related to exponential and power-law Lagrangian, are explored and presented. The variational principles for the Chaplygin systems with nonstandard Lagrangian are derived, and the generalized Chaplygin equations for the corresponding systems are established, the Noether transformations are considered, from which the corresponding conserved quantities are deduced. And their inverse theorems for nonstandard generalized Chaplygin systems are given. Two examples show the validity of the results.

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Title: Noether theorem and its inverse for nonstandard generalized Chaplygin systems
Authors: S. X. Jin
Y. M. Li
X. W. Chen
Publication date: 10-12-2023
Publisher: Springer Vienna
Published in: Acta Mechanica / Issue 2/2024
Print ISSN: 0001-5970
Electronic ISSN: 1619-6937
DOI: https://doi.org/10.1007/s00707-023-03812-y

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Noether theorem and its inverse for nonstandard generalized Chaplygin systems

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