Studies On The Multi-scale Method And Jacobi Solution

In this paper we mainly research the multi-scale method of tokamak system andelectromagnetic bearing system and the tokamak system's jacobi solution. Fistly, wereviewe the reaserch backgroud and status of nonlinear dynamic, the multi-scalemethod, concerns of their present achievements. Sencondly, the theories of nonlineardynamic, the multi-scale method, long item, and the jacobi elliptic function methodare introduced. And, in chapter four and chapter five, the main contents of this paperare put forward. The focus are as follows:(1) By using the multi-scale method, we research the tokamak system andelectromagnetic bearing system, and through parameter control we obtain theconsistence conditions of the same degree items of these two systems' averagefunction -third order average function in one scale and fifth order average function intwo scales.(2) We use jacobi elliptic function method to find the analytical solution ofTokamak equation, which satisfies the consistence condition of the same degree itemsof the average function. And by using maple software, we get the structure diagram ofthe solution. It has important meaning and applied value to the practical research.Finally, we introduce the hot issues concerned with multi-scale and jacobisolution method. Combining with the main research achievements of this paper wepoint out the further research direction and prospect.