Abstract

The use of elliptic integrals is required to solve many problems of mechanics and geophysics, even though it is laborious to express them analytically. For calculating elliptic integrals of the first and second kind, new and improved analytical dependencies are provided in terms of elementary functions, the values of which are in good agreement (~1–2%) with the results of known exact solutions, coinciding with them for the boundary conditions. As a basic practical example of using the formulas obtained, the nonlinear problem of determining the arc length of a sinusoid (cosinusoid) is solved, making it possible to identify sections with nonlinear and linear length change.

中文翻译：

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力学非线性问题中的椭圆积分

摘要

尽管解决方案很难解析，但仍需要使用椭圆积分来解决许多力学和地球物理学问题。为了计算第一类和第二类椭圆积分，根据基本函数提供了新的和经过改进的解析相关性，其依赖项与已知精确解的结果具有很好的一致性（约1-2％）。边界条件。作为使用所获得的公式的基本实践示例，解决了确定正弦曲线（cosinusoid）的弧长的非线性问题，从而可以识别具有非线性和线性长度变化的截面。