约束系统的变换性质

受约束的系统,它的运动可用非独立的态函数来描述。在约束系统的时空坐标和态函数作无穷小变换下,考虑到作用量和约束方程的变化,导致了普遍的变换结果,沿着系统运动的轨线,得到约束系统变换性质的一般方程,从而给出约束系统在变换下产生守恒律的条件,对连续系统的某些具体变换写出了其变换性质方程,在特殊情况下,变换性质方程可化为经典Noether定理的结果,用于经典力学作了较详细的讨论,并把Poincaré-Cartan不变量推广到了受约束系统。 关键词：

THE TRANSFORMATION PROPERTIES OF CONSTRAINED SYSTEM

The motion of constrained system may be described in terms of non-independent state functions. We considered the change of the action integral and constraint equations under the infinitesimal transformation of the time-space points and state functions of the constrained system, this leads to the general transformation result. We obtained the general equations for the transformation properties of constrained system along the trajectory of motion of that system. From these equations, the condition under which the transformation of constrained system yields conservation law can be worked out. For some specific transformations of the continuous system, we have found the equations of transformation properties. In the special cases, the general equations of transformation properties can be reduced to the results the classical Noether's theorem, The application of general results to classical mechanics is discussed in detail and the Poincare-Cartan invariant is generalized to the constrained system.