马丢的英文
mathieu
例句与用法
- From the exact expression of the field , we obtain a multipole polynomial expansion , and under the paraxial condition we furthermore obtain the approximate expression . the loffe trap , consisting of two coils with parallel currents and four straight conductors with currents in alternating directions , is one of the most important traps . we specially study the field structure of it by using both the exact expression and a multipole polynomial expansion that facilitates studies of classical or quantum orbits . if the region near the origin is of interest , we may obtain a simple expression of the field and this configuration may be called idealized loffe trap
若只讨论阱中的近原点区域时，阱中的磁场可以呈现出一种简洁的形式，人们把它称为理想ioffe阱。磁矩反平行于磁场的中性粒子在阱中与磁场发生相互作用，借助相互作用势，可以获得粒子在阱中的经典运动方程。在一定的近似条件下，我们可以采用逐次近似的方法，使方程简化，其中三个分量式中关于z的方程比较容易求解，而关于x 、 y的方程则演化为我们熟悉的马丢方程的形式。 - 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
若阱的参数设置使得条件> > q 0成立时，我们可以利用传统的wkbj方法近似求解马丢方程。作为一种新的尝试，本文还采用傅立叶级数展开的办法来对马丢方程进行求解，从而得到中性粒子在阱中的经典运动规律。在研究ioffe阱对中性粒子的囚禁问题时，实际上我们更感兴趣的是马丢方程的周期解，而要想获得这种周期解，和q必须满足一定的关系，亦即必须选择阱的特定的参数和粒子的特定初始条件，对这一问题我们进行了尝试性的研究。 - The major achievements are listed as the followings : mathieu functions remain difficult to employ , mainly because of the impossibility of analytically representing them in a simple and handy way . the methods for the computation of all mathieu functions of integer orders for large range of the order n and the parameter q were presented here . the calculations were made by programs using matlab to compute the mathieu functions
本论文的主要工作:由于在使用马丢函数时存在一些困难,主要是因为不能简单方便地对其进行解析表示,我们给出整数阶各类马丢函数的详细计算方法,该方法适合较大范围的阶数n和参数q值,实际计算中采用了matlab软件进行编程实现,并给出了各类马丢函数在自变量和q值两个参数变化下的三维可视化图形。 - Then , use galerkin principle to put the stability equation in order for the special function the mathieu standard form , and utilize the boundary of the mathieu solves ’ steady area and unsteady area , namely special relationships of and , draw the discrimination equation of losing the magnetoelastic steady critical state
然后，应用galerkin原理将稳定性方程整理为特殊函数马丢方程的标准形式，并利用马丢方程的稳定解区域与非稳定解区域的分界，即系数和的本征值关系得出了磁弹性最低失稳临界状态的判别方程。
