本文選題：鐘擺 + 極限環(huán)��； 參考：《江蘇大學(xué)》2017年碩士論文

【摘要】：分段光滑系統(tǒng)作為一類典型的非線性系統(tǒng),其相關(guān)的理論在自然科學(xué)和社會科學(xué)領(lǐng)域都有廣泛的應(yīng)用,許多科學(xué)問題都需要用分段光滑動力系統(tǒng)理論來分析研究。本文以帶有干摩擦和沖擊效應(yīng)的鐘擺為研究背景,探索了一般的鐘擺模型的極限環(huán)的存在性。首先結(jié)合Filippov系統(tǒng)刻畫語言,解釋了當鐘擺進行無外加能量補充的小擺角擺動時,鐘擺最終會停止在滑動集上的原因。其次,利用數(shù)值模擬的方法,給出鐘擺系統(tǒng)在有能量補充時,存在極限環(huán)的能量滿足條件,并結(jié)合環(huán)域定理證明了一般的鐘擺模型存在唯一穩(wěn)定的極限環(huán)。最后,本文在含參數(shù)分段線性系統(tǒng)的極限環(huán)存在的基礎(chǔ)上,研究了一類含參數(shù)分段非線性系統(tǒng),當參數(shù)從大于0變化到小于0過程中,系統(tǒng)的平衡點由結(jié)點移動到焦點時,系統(tǒng)極限環(huán)存在的條件及證明。
[Abstract]:As a typical nonlinear system, piecewise smooth systems are widely used in both natural and social sciences. Many scientific problems need to be analyzed and studied by piecewise smooth dynamical system theory. Based on the pendulum with dry friction and impact effects, the existence of limit cycles of general pendulum models is explored in this paper. Firstly, with the Filippov system description language, it is explained why the pendulum will eventually stop on the sliding set when the pendulum oscillates at a small angle without additional energy. Secondly, by using the numerical simulation method, we give the condition that the energy of the pendulum system has limit cycle when there is energy supplement, and prove that there is a unique stable limit cycle in the general pendulum model combined with the theorem of ring domain. Finally, based on the existence of limit cycles of piecewise linear systems with parameters, this paper studies a class of piecewise nonlinear systems with parameters. When the parameters change from 0 to less than 0, the equilibrium point of the system moves from node to focus. The condition and proof of the limit cycle of the system.
【學(xué)位授予單位】：江蘇大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O175

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1 岳錫亭;關(guān)于二次系統(tǒng)極限環(huán)的分布[J];吉林工學(xué)院學(xué)報(自然科學(xué)版);2002年01期

2 梁錦鵬;一類三次系統(tǒng)的極限環(huán)[J];系統(tǒng)科學(xué)與數(shù)學(xué);2003年03期

3 王國棟,唐衡生,陳文成;一類2n-1次系統(tǒng)的極限環(huán)[J];南華大學(xué)學(xué)報(理工版);2003年02期

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