Abstract
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.
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