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In this paper, we eliminate the coupled terms in Lagrangian firstly by changing the coordinate scales and rotating the coordinate axes, and obtain the conserved quantities in new coordinates directly. According inverse transform of the coordinates, we can obtain the conserved quantities in original coordinates, the Noether symmetry and Lie symmetry of the infinitesimal transformations of conserve quantities are studied in this paper，and an example is given to illustrate the application of the result.
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Keywords:
- linear coupled multidimensional freedom systems /
- conserved quantities /
- Noether symmetry /
- Lie symmetry
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