子午线弧长反问题新解
New Solutions on Inverse Problem of Meridian Arc
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摘要: 针对子午线弧长反解计算过于繁琐的问题,利用复合函数的求导法则,变换变量进行幂级数展开,给出了通项公式,利用Hermite插值原理推导了各参数,借助Mathematica计算机代数系统,得出了这些公式用偏心率e表示的幂级数表达式。经试算其精度在0.001″以上,可供实际使用。Abstract: Making use of derivative rule of complex functions,how to compute a foot point latitude in ellipsoidal geodesy by Taylor expansion is described.The general expression of the foot point latitude expansion is presented.For comparison,based on the principle of Hermite interpolation,each parameter of the formula can be obtained by Mathematica.The numerical investigation shows that the formulas described are sufficiently accurate up to 0.001″.
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