本文選題：不連續(xù)動力系統(tǒng) + 流轉(zhuǎn)換��； 參考：《山東師范大學(xué)》2017年碩士論文

【摘要】：不連續(xù)現(xiàn)象在現(xiàn)實(shí)生活中普遍存在,如:摩擦問題、碰撞問題、脈沖問題等.而隨著學(xué)者們對不連續(xù)動力系統(tǒng)的研究逐漸深入,我們意識到,連續(xù)動力系統(tǒng)可以視為不連續(xù)動力系統(tǒng)的特殊情況,對以上不連續(xù)現(xiàn)象中若干問題的研究都可以轉(zhuǎn)化為研究與之對應(yīng)的不連續(xù)動力系統(tǒng).由此可見,對不連續(xù)動力系統(tǒng)的研究尤為重要.脈沖系統(tǒng)作為不連續(xù)動力系統(tǒng)的一種特殊情況,我們很自然地想運(yùn)用不連續(xù)動力系統(tǒng)的工具來解決脈沖微分系統(tǒng)的一個(gè)經(jīng)典問題——脈沖微分系統(tǒng)的脈動現(xiàn)象.此外,如前所述,研究不連續(xù)動力系統(tǒng)可以解決我們生活中的許多問題,因此本文便想運(yùn)用不連續(xù)動力系統(tǒng)的流轉(zhuǎn)換理論研究生活中的一個(gè)具體問題.基于此,全文分為兩章.在第一章中,主要研究如下具依賴狀態(tài)的脈沖微分系統(tǒng) 其中F∈C(R+×Ω, R~n),開集Ω(?)R~n,X = (x1,x2, ...,xn)T ∈Ω,τ ∈C1(R~n,R+),H ∈C1(R~n,R~n),I ∈C(Ω,R~n).假設(shè)當(dāng)x ∈ Ω時(shí),有x + I(X) ∈ Ω.通過將系統(tǒng)(1.2.1)視為一個(gè)包含兩個(gè)連續(xù)子系統(tǒng)的不連續(xù)動力系統(tǒng),運(yùn)用不連續(xù)動力系統(tǒng)的流轉(zhuǎn)換理論,得到脈動現(xiàn)象發(fā)生和消失的幾個(gè)充分條件.特別地,解在脈沖面上滑行的情況真實(shí)存在并在同步問題中有重要的應(yīng)用,但這又超越了古典意義上脈沖微分系統(tǒng)解的定義,故我們在本章中對此給出了新的定義,并給出了幾個(gè)其發(fā)生的充分條件.本章得到的關(guān)于脈動現(xiàn)象發(fā)生和消失的結(jié)果較用經(jīng)典方法得到的結(jié)果,對脈沖函數(shù)T的要求降低.在第二章中,我們建立了一個(gè)針對某些裝置連接問題的新的物理模型——受周期激勵(lì)的圓弧碰撞振子,根據(jù)動量守恒定律、碰撞定律、圓周運(yùn)動規(guī)律、小球運(yùn)動的水平分量與切向運(yùn)動量之間的關(guān)系以及在本章中定義的小球的角位移,建立了此振子在不同運(yùn)動狀態(tài)下的運(yùn)動方程.根據(jù)碰撞引起的不連續(xù)性,定義了不同的運(yùn)動區(qū)域和邊界,基于此,運(yùn)用不連續(xù)動力系統(tǒng)的流轉(zhuǎn)換理論,給出了圓弧碰撞振子粘合運(yùn)動和擦邊運(yùn)動的充要條件,得到了體現(xiàn)圓弧碰撞振子本質(zhì)特點(diǎn)的新結(jié)果,此結(jié)果展現(xiàn)了較水平碰撞振子、豎直碰撞振子和斜面碰撞振子更加復(fù)雜、豐富的動力學(xué)行為.
[Abstract]:Discontinuity exists in real life, such as friction problem, collision problem, pulse problem and so on. However, as the research of discontinuous dynamic system has gradually deepened, we realize that continuous dynamic system can be regarded as a special case of discontinuous dynamic system. The study of some problems in the above discontinuous phenomena can be transformed into the corresponding discontinuous dynamical systems. Therefore, the study of discontinuous dynamic system is particularly important. Impulsive systems as a special case of discontinuous dynamical systems, we naturally want to use discontinuous dynamical systems tools to solve a classical problem of impulsive differential systems-impulsive differential system pulsation phenomenon. In addition, as mentioned earlier, the study of discontinuous dynamical systems can solve many problems in our life, so this paper intends to use the theory of flow transformation of discontinuous dynamical systems to study a specific problem in life. Based on this, the full text is divided into two chapters. In the first chapter, the following impulsive differential systems with dependent states are studied, where F 鈭，

本文編號：2025787