For small displacement u , the oscillator is a duffing - type cubic non - linear oscillator , while for large displacement u , the oscillator approximates to a linear harmonic oscillator 所謂達(dá)芬諧波振子是指當(dāng)位移遠(yuǎn)小于1時(shí),系統(tǒng)可化為三次非線(xiàn)性振子,而當(dāng)位移遠(yuǎn)大于1時(shí),該系統(tǒng)則化為線(xiàn)性諧波振子。
The author has calculated the spontaneous radiate probabilities , the linear oscillator strengths , branching ratio of tm3 + iones by judd - oflet theory . according to the j - o calculated data , the transition 1g4 ? 3h6 was stronger than the transition 1g4 ? 3h4 . it was agreement with the emission spectra 3 )對(duì)tbzre玻璃,用j ? o理論計(jì)算了各光譜參數(shù),從1g4能級(jí)的躍遷分支比從理論上得出480nm波長(zhǎng)的光相對(duì)650nm波長(zhǎng)的光強(qiáng),這與發(fā)射光譜圖是相符合的。
In order to prove the existence of the periodic boucing solutions , firstly we will introduce a new coordinate transformation , transform the system from right half plane to the whole plane . and give the relation of the eigenvalues of hill ' s equation and the rotation numbers , using this approach and pioncar - birkhoff twist theorem , we proved the existence of the periodic bouncing solutions for asymptotical linear oscillator 對(duì)于周期解的存在性證明,我們引進(jìn)新的坐標(biāo)變換把右半平面上的碰撞問(wèn)題轉(zhuǎn)化到整個(gè)平面上,給出旋轉(zhuǎn)數(shù)與hill方程的特征值的關(guān)系,并以此來(lái)度量漸近線(xiàn)性振子,再應(yīng)用pioncar - birkhoff扭轉(zhuǎn)定理得到周期碰撞解的存在性。
Impact oscillator is an important model of nonsmooth dynamical system . in this article , we study the dynamics of elastic imapact oscillators . we will consider the asymptotically linear oscillator and study it in two parts : the existence of periodic bouncing solutions ; the lagrange stability of impact motion 碰撞振子是非光滑動(dòng)力系統(tǒng)中一類(lèi)重要模型,本文討論彈性碰撞振子的動(dòng)態(tài)行為,主要考慮漸近線(xiàn)性振子的碰撞解,文章分兩部分:周期碰撞解的存在性;碰撞運(yùn)動(dòng)的lagrange穩(wěn)定性。