一类多自由度线性耦合系统的对称性与守恒量研究

运用改变坐标标度和旋转坐标轴的方法先消去Lagrange函数中的耦合项，直接得到新坐标系下的守恒量，利用坐标反变换得到原坐标系下的守恒量，并讨论与守恒量相应的无限小变换的Noether对称性与Lie对称性，最后举例说明结果的应用.关键词：多自由度线性耦合系统守恒量Noether对称性Lie对称性

The study of symmetries and conserved quantities for one class of linearly coupled multidimensional freedom systems

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.