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本文将Bjerhammar换置推广到顾及椭球扁率一级效应的情况,以便适应获得高精度计算结果的特殊目的。为了实现这一推广,遵循如下途径:(a)导出含椭球扁率效应的新的Poisson积分;(b)求解径向微商边界条件的所谓简单的椭球Robin问题;(c)通过从法向微商到径向微商的边界条件交换,借助于简单Robin问题的解,导出一般的椭球Robin问题的解案。最后,将广义的Poisson积分应用到正则调和函数r△g,将一般的Robin问题的解应用到椭球情况下的线性化Molodensky问题,并将两者联合,便得到所求的椭球情况的换置。很明显,若设扁率为零,本文得到的换置则蜕化为传统的换置。
In this paper, the Bjerhammar commutation is extended to take account of the first-order ellipsoidal oblateness effect in order to adapt to the special purpose of obtaining high-precision computational results. In order to achieve this promotion, the following approaches are followed: (a) to derive new Poisson integrals with ellipsoidal oblateness effects; (b) to solve the so-called simple ellipsoid Robin problem of radial derivative conditions; (c) The exchange of the boundary conditions between the normal derivative and the radial derivative and the solution of the general elliptic Robin problem are derived by means of the solution of the simple Robin problem. Finally, the generalized Poisson integral is applied to the regular harmonic function r △ g, the general solution of Robin’s problem is applied to the linearized Molodensky problem in the ellipsoid case, and the two are combined to obtain the ellipsoid situation Replacement. Obviously, if the flat rate is set to zero, the transposition obtained in this paper degenerates into the traditional replacement.