Noether`s inverse theorem of Birkhoffian system was studied. The general solution that Noether`s 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.
丁光涛. Birkhoff系统Noether逆定理的解法[J].动力学与控制学报,2010,8(2):100~104; Ding Guangtao. The solutions for noether`s inverse theorem of birkhoffian system[J]. Journal of Dynamics and Control,2010,8(2):100-104.