椭圆弧长的级数表达式及其近似计算

Series Expansion and Approximate Treatment for Elliptic Arc Length

导出了以椭圆参数方程离心角为变量的椭圆弧长级数表达式,可以计算任意离心角对应的椭圆弧长;在级数表达式基础上归纳了椭圆弧长近似计算公式,为解决实际应用问题提供了方便.

Derived series expansion for elliptic arc length by taking eccentric angle in the elliptic parameter equation as a variable.By using this expansion,the elliptic arc length corresponding to any centrifugal angle can be calculated.On the basis of the series expression,elliptic arc length approximation formulas are summarized,and these formulas provide convenience on solving practical application problems.