约束系统的对称变换

对于用非独立态函数描述的受约束系统,在对称变换下将导致推广的Noether定理,一般说,此时不产生Noether定理的守恒量,在有限约束下内部对称变换的推广Noether定理,就化为通常Noether定理的结果。关键词：

THE SYMMETRY TRANSFORMATIONS OF THE CONSTRAINED SYSTEM

The motion of constrained system may be described in terms of the non-independent state functions. Suppose the action integral and constraint conditions of this system are invariant under the symmetry transformations of the time-space points and state functions, then we can generalize the Noether's theorem to this constrained system. In general, it does not yield the conservation laws as ordinary Noether's theorem. However, when the system only subjects to finite constraint, the generalized Noether's theorem can reduce to the results as ordinary Noether's theorem.