The Many Faces of Elastica by Ivaïlo M. Mladenov & Mariana Hadzhilazova

Author:Ivaïlo M. Mladenov & Mariana Hadzhilazova
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(4.33)

where the numerical factors are given by the expressions

(4.34)

while and denote the so-called incomplete elliptic integrals of, respectively, the first and second kinds, which are functions of their argument , and the parameter k is known as an elliptic modulus.

Let us also consider the case in which the differential hydrostatic pressure across the membrane vanishes, i.e., . In that case, the intrinsic equation (4.30) reduces to

(4.35)

and its solution is

(4.36)

This time, (4.28) and (4.27) produce the parameterization of the catenoid

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