Comment on ‘Elliptic integral solutions of spatial elastica of a thin straight rod bent under concentrated terminal forces’

Abstract

In a recent paper published in Meccanica [1] it is claimed that solutions of the equilibrium equations for the spatial elastica are given in explicit form. I would like to point out that such solutions are not new and already published elsewhere. In the title, in the abstract and in the conclusion of [1] it is claimed that, analytical, closed-form solutions of the nonlinear equations for the elastica in space are given for the first time. In this sense equations (6), (9), and (14) are the main result of the paper. I would like to point out that closed-form solutions of the spatial elastica are known, and that equations (6), (9), and (14) are (a sub-case of) equations (21), (27), and (20) of a published paper [2]. It is rather confusing to notice that this paper [2] is cited in [1]! More precisely, the scheme which is followed in [1] (i.e. passing to cylindrical coordinates, translation of the reference frame, etc.) is thoroughly explained in [2] (Sect. 2, pp. 10991–10993). In fact, the scheme was introduced (as far as I know) in the book by Landau and Lifshitz [3] (see Problem 5 of Sect. 19: The equations of equilibrium of rods).