The study of symmetries and conserved quantities for one class of linearly coupled multidimensional freedom systems
一类多自由度线性耦合系统的对称性与守恒量研究

In this paper, we eliminate the coupled terms in I~grangian 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 conserved quantities are studied in this paper, and an example is given to illustrate the application of the result.