准坐标下的非完整非保守力学系统的Noether理论

给出了准坐标下的受一阶非线性非完整约束的非保守动力学系统的Nocther定理、逆定理及其守恒存在的条件。结果表明,在准坐标下,无穷小变换的生成函数不必附加 定义的条件限制,而在广义坐标下是必须附加这个限制的,从而显示出采用准坐标具有明显的优点。

NOETHER''''S THEORY OF NONHOLONOMIC NONCONSERVATIVE DYNAMICAL SYSTEMS UNDER QUASI - COORDINATES

Noether's theorem, Noether's inverse theorem and the existent conditions of conservative quantity of nonconservative dynamical systems subjected to one-order nonlinear nonholonomic constraints under quasi-coordinates were studied. Results indicated that under quasi-coordinates, the generating functions of infinitesimal transformations were not subjected to restriction of Chetaev's definition, while under generalized coordinates, this restriction must be attached. Therefore, using, quasi-coordinates could have an advantage over using generalized coordinates.