Sn,Cn,Dn波导的研究

Studies on Sn,Cn and Dn Waveguides

Sn函数是一种正弦函数,Cnu、dnu则类似余弦函数(Cayley),而圆函数sinu、cosu是单周期的,Snu、Cnu、Dnu则是双周期的。Snu有两个焦点对±1及±1/k,Cnu有两个焦点对±1及±jk′/r,而dnu也有两个焦点对±1及±k′,故动点至这些焦点对有4个距离,它们之间的和差关系是我们要研究的对象,以便计算决出动点的轨迹。

The function Snu is a sort of sine function and Cnu, Dnu are sorts of cosine functions（ Cayley）, but sinu, cosu are single periodic circular functions, Snu, Cnu, Dnu are doubly periodic functions. Snu has two focal pairs ± 1,±1/k; Cnu has two focal pairs ±1 and ±jk＇/k,Dnu has two focal pairs ±1 and ± k＇, so a moving point will have four distances to each two pairs of focal pairs, how are the sums and differences are related, so how is the locus of the moving point？ Those are to be investigated.