Lie Symmetrical Non-Noether Conserved Quantity of Mechanical System in Phase Space

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In this paper, we study the Lie symmetrical non-Noether conserved quantity of the differential equations ofmotion of mechanical system in phase space under the general infinitesimal transformations of groups. Firstly, we givethe determining equations of the Lie symmetry of the system. Secondly, the non-Noether conserved quantity of the Liesymmetry is derived. Finally, an example is given to illustrate the application of the result.
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