Birkhoff系统Noether逆定理的解法

THE SOLUTIONS FOR NOETHER'S INVERSE THEOREM OF BIRKHOFFIAN SYSTEM

研究Birkhoff系统Noether逆定理.提出对Birkhoff系统由已知的守恒量导出Noether对称性的一般解法,指出一般解法中的困难.通过引入守恒量和对称性直接相关的辅助方程,给出逆定理的特殊解法.举例说明了所得结果的应用.

Noether′s inverse theorem of Birkhoffian system was studied.The general solution that Noethers symmetries can be deduced from the known conserved quantities for Birkhoffian system was proposed.The difficulties in the general solution were pointed.The special solutions for the inverse theorem were presented by introducing auxiliary equations,in which the conserved quantity and the symmetry are interrelated directly.An example was given to illustrate the application of the results.