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.
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