VARIOUS CENTROIDS AND SOME CHARACTERIZATIONS OF CATENARY CURVES

Abstract

For every interval [a, b], we denote by ((x) over bar (A), (y) over bar (A)) and ((x) over bar (L), (y) over bar (L) the geometric centroid of the area under a catenary curve y = k cosh((x - c)/k) defined on this interval and the centroid of the curve itself, respectively. Then, it is well-known that (x) over bar (L) - (x) over bar (A) and (y) over bar (L) = 2 (y) over bar (A). In this paper, we fix an end point, say 0, and we show that one of (x) over bar (L) = (x) over bar (A) and (y) over bar (L) = 2 (y) over bar (A) for every interval with an end point 0 characterizes the family of catenaries among nonconstant C-2 functions.