First order approximate conserved quantities induced by the approximate symmetries of the perturbed Lagrangian

The conserved quantities of the approximate symmetries of perturbed Lagrange systems are investigated in this article. The research first finds new conserved quantities directly, which are induced by the approximate Lie symmetry of perturbed Lagrange systems, and sheds light on their precise form and prerequisites for existing. The second part of the article looks at the relationships between Noether, Mei, and Lie approximate symmetries and emphasizes how these approximate symmetries can be used to infer these novel kinds of conserved quantities. The piece concludes with an illustration of some examples.& COPY; 2023 Elsevier B.V. All rights reserved.

Automated summary

This article investigates the conserved quantities of the approximate symmetries of perturbed Lagrange systems. The research discovers new conserved quantities induced by the approximate Lie symmetry of perturbed Lagrange systems and provides insights into their precise form and prerequisites. Additionally, it explores the relationships between Noether, Mei, and Lie approximate symmetries and highlights their use in inferring novel types of conserved quantities. The article concludes by illustrating some examples.