引潮位展开中的面球谐函数及其递推公式

RECURRENCE RELATIONS OF THE SURFACE SPHERICAL HARMONICS IN THE DEVELOPMENT OF THE TIDAL GENERATING POTENTIAL

为了引潮位展开，文中定义了一种完全规格化的面球谐函数，同时根据勒让德（Ｌｅｇｅｎｄｒｅ）函数以及契比雪夫（Ｃｈｅｂｙｓｈｅｖ）多项式之递推公式，导出一组面球谐函数的递推公式．据此改进引潮位计算程序，使引潮位展开在ＰＣ－５８６计算机上只需要不到１０ｍｉｎ时间即可完成．完全规格化的面球谐函数可以起到规格化的作用，没有必要再继续采用杜德森（Ｄｏｏｄｓｏｎ）规格化．即使采用，也没有必要使用严格的小数值，取其相近的整数值即可．以完全规格化的缔合球谐函数代替Ｄｏｏｄｓｏｎ规格化，并借助面球谐函数的递推公式，使引潮位的表达式更加简洁、规范．文中对高精度潮汐计算中的一些重要问题进行了讨论，指出以往在Ｄｏｏｄｓｏｎ常数归算上存在的误区，还就天体与测站坐标系统的一致性问题进行了讨论．

A fully normalized associated Legendre function has been defined by author forthe development of the tidal generating potential, and a set of recurrence relations ofthe surface spherical harmonica has been deduced from the recurrence relations of the Legendre function and the Chebyshev polynomial. According to that the programs fordevelopment of the tide generating potential (TGP) have been developed, so thedevelopment of the TGP can be rapidly doen in less than 10 minutes on a 586 PC. The fully normalized associated Legendre function has taken an effect of thenormalization, so lt is not necessary to adopt the Doodson normalization, even if onehas to use that it is also not necessary to adopt a decimal value, an integer valuesapproximating to that are enough. The fully normalized associated Legendre functionmay be used to instead of the Doodson mormalization, Using the recurrence relationswill make the expression of the tide potential simple and standard. In this paper someimpotent problems on high preciesion tidal data processing are discussed.A mistakedue to recalculating the Doodson constant is pointed. The identity of the referencesystem of the celestial body and the station is discussed also.