發(fā)布時(shí)間：2018-04-25 11:54

  本文選題：無(wú)窮維Hamilton正則系統(tǒng) + 循環(huán)算子�。� 參考：《內(nèi)蒙古工業(yè)大學(xué)》2017年碩士論文

【摘要】：無(wú)窮維Hamilton系統(tǒng)是一類具有特殊結(jié)構(gòu)的偏微分方程(組),是解決物理、力學(xué)、控制等實(shí)際問(wèn)題常用的基本形式.本文在Hamilton系統(tǒng)這個(gè)框架下,主要針對(duì)循環(huán)算子的獲得和反問(wèn)題進(jìn)行了探討,首先將一般微分方程系統(tǒng)的循環(huán)算子的某些理論平移到Hamilton體系中,得到一種獲得循環(huán)算子的方法;然后對(duì)無(wú)窮維Hamilton系統(tǒng)的反問(wèn)題的作了兩點(diǎn)探討.第一章,首先簡(jiǎn)述了研究對(duì)象及Hamilton系統(tǒng)的大致研究方向,并羅列了一些與無(wú)窮維Hamilton系統(tǒng)相關(guān)的定義;其次,闡述循環(huán)算子研究現(xiàn)狀并對(duì)反問(wèn)題方法作了綜述;最后,介紹了全篇的主要研究思路及工作.第二章,對(duì)Hamilton系統(tǒng)循環(huán)算子的獲得方法作出了探索,主要是將一般微分方程系統(tǒng)循環(huán)算子的一個(gè)結(jié)論移植到無(wú)窮維Hamilton系統(tǒng),獲得了常型Hamilton系統(tǒng)下循環(huán)算子的一般結(jié)論,并通過(guò)算例驗(yàn)證了該結(jié)論的可行性.第三章,在前人研究的基礎(chǔ)上,對(duì)Hamilton系統(tǒng)的反問(wèn)題作了兩點(diǎn)探討,第一,基于Taylor展開(kāi)式的基礎(chǔ)上改進(jìn)了狀態(tài)變量的計(jì)算方法,其簡(jiǎn)便性主要體現(xiàn)在分解因子Q的系數(shù)的計(jì)算上;第二,對(duì)文獻(xiàn)已討論過(guò)的一類Hamilton算子決定的高階方程的正則化作了探索,并通過(guò)尋找變換,實(shí)現(xiàn)了一類新Hamilton算子決定的方程的正則形式化問(wèn)題.最后,對(duì)所做的工作進(jìn)行了一些簡(jiǎn)單地總結(jié),分析出其中的不足之處,并對(duì)接下來(lái)可能開(kāi)展的工作指明了方向.
[Abstract]:Infinite dimensional Hamilton system is a kind of partial differential equation with special structure, which is a basic form of solving practical problems such as physics, mechanics, control and so on. In this paper, under the framework of Hamilton system, we mainly discuss the problem of obtaining and inverse cyclic operators. Firstly, some theories of cyclic operators of general differential equation systems are translated into Hamilton system, and a method of obtaining cyclic operators is obtained. Then the inverse problem of infinite dimensional Hamilton system is discussed in two aspects. In the first chapter, the research object and the general research direction of Hamilton system are briefly introduced, and some definitions related to infinite dimensional Hamilton system are listed. Secondly, the research status of cyclic operator and the method of inverse problem are summarized. This paper introduces the main research ideas and work of the whole article. In the second chapter, the method of obtaining cyclic operators for Hamilton systems is explored. A conclusion of cyclic operators for ordinary differential equation systems is transplanted to infinite dimensional Hamilton systems, and the general results of cyclic operators in Hamilton systems of constant type are obtained. The feasibility of the conclusion is verified by an example. In chapter 3, the inverse problem of Hamilton system is discussed on the basis of previous studies. Firstly, the calculation method of state variables is improved on the basis of Taylor expansion, and its simplicity is mainly reflected in the calculation of the coefficient of decomposition factor Q; Secondly, the regularization of a class of higher order equations determined by Hamilton operators, which has been discussed in the literature, is explored. By searching for transformations, the regularization formalization of a class of equations determined by new Hamilton operators is realized. Finally, the work done is summarized briefly, the shortcomings are analyzed, and the direction of the possible work is pointed out.
【學(xué)位授予單位】：內(nèi)蒙古工業(yè)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O175.2

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本文編號(hào)：1801199