Chaos controlling for a kind of mathieu equation 方程的混沌控制
Chaos controls on mathieu equations 方程的混沌控制
Mathieu equation and dynamic stabilities for cyclotron with 4 - folded symmetry 度對(duì)稱(chēng)徑向扇回旋加速器的動(dòng)力學(xué)穩(wěn)定性
We consider a neutral particle with magnetic moment antiparallel to the field . with the interaction potential energy between the magnetic moment of the particle and the magnetic field , we obtain the classical motion equation of the neutral particles in the loffe trap . in some limit conditions , by using the perturbative method , the equations may take on concise forms . of which the two equations about x and y are mathieu equations . if we properly set the parameters and have the condition a > > q > 0 , we can solve the mathieu equation with the traditional wkbj method . as a new attemptation , with fourier series expansion we solve the mathieu equation and obtain the classical motion law of the neutral particles 若阱的參數(shù)設(shè)置使得條件> > q 0成立時(shí),我們可以利用傳統(tǒng)的wkbj方法近似求解馬丟方程。作為一種新的嘗試,本文還采用傅立葉級(jí)數(shù)展開(kāi)的辦法來(lái)對(duì)馬丟方程進(jìn)行求解,從而得到中性粒子在阱中的經(jīng)典運(yùn)動(dòng)規(guī)律。在研究ioffe阱對(duì)中性粒子的囚禁問(wèn)題時(shí),實(shí)際上我們更感興趣的是馬丟方程的周期解,而要想獲得這種周期解,和q必須滿(mǎn)足一定的關(guān)系,亦即必須選擇阱的特定的參數(shù)和粒子的特定初始條件,對(duì)這一問(wèn)題我們進(jìn)行了嘗試性的研究。