三个耦合摆微幅振动的守恒量与对称性研究

The study of conserved quantities and symmetries for microvibration of three coupled pendulums

用拉格朗日方程建立三个耦合摆在微幅振动下的运动微分方程,通过坐标变换实现对拉格朗日函数的解耦,从而直接求得系统的4个守恒量,并运用Noether逆定理和Lie对称性理论分析与守恒量相应的Noether对称性和Lie对称性.

The kinematic differentiation equations of microvibration of three coupled pendulums are obtained by using Lagrangian equations,we decouple the Lagrangian by transforming coordinates and obtain directly four conserved quantities from uncoupled Lagrangian. The Noether symmetries and Lie symmetries of four conserved quantities are studied by using inverse Noether theorem and Lie symmetry theorem.