准坐标下广义非保守系统Lagrange方程的积分因子与守恒定理

Integrating factors and conservation theorems of Lagrange's equations for generalized nonconservative systems in terms of quasi-coordinates

用积分因子方法研究准坐标下广义非保守系统Lagrange方程的守恒定理.列写系统的运动微分方程,给出它的积分因子的定义.研究守恒量存在的必要条件.建立系统的守恒定理及其逆定理,并举例说明结果的应用.

The conservation theorems of the Lagrange＇ s equations for generalized nonconservative systems in terms of quasi-coordinates are studied by using the method of integrating factors. The differential equations of motion of systems are written. The definition of integrating factors is given. The necessary conditions for the existence of the conserved quantity are studied in detail. Finally, the conservation theorem and its inverse are established, and an example is given to illustrate the application of the result.