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Noether theorem and its inverse for nonstandard generalized Chaplygin systems

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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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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 12102241 and 11572212).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Shangqiu Normal University, Shangqiu, 476000, Henan, China

    S. X. Jin

  2. School of Physics and Information Engineering, Shangqiu Normal University, Shangqiu, 476000, Henan, China

    Y. M. Li & X. W. Chen

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  1. S. X. Jin
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  2. Y. M. Li
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  3. X. W. Chen
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Contributions

S-XJ: Conceptualization, Methodology, Validation, Formal analysis, Visualization, Writing-review & editing, Supervision, Project administration, Funding acquisition. Y-ML: Conceptualization, Methodology, Writing-original draft. X-WC: Conceptualization, Methodology, Writing-original draft.

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Correspondence to S. X. Jin.

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Jin, S.X., Li, Y.M. & Chen, X.W. Noether theorem and its inverse for nonstandard generalized Chaplygin systems. Acta Mech 235, 1361–1373 (2024). https://doi.org/10.1007/s00707-023-03812-y

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  • DOI: https://doi.org/10.1007/s00707-023-03812-y

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