Hanging chain (catenary)

Realizes: hyperbolic cosine / thrust line

A chain suspended from two fixed points and left to hang under gravity settles into a curve that exactly realizes the hyperbolic cosine. Gaudí used physical catenaries (inverted) to design the arches of the Sagrada Família. Speed: instantaneous (static equilibrium). Capacity: single function evaluation (hyperbolic cosine).

Examples

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Gaudi: Flipping Catenaries

How Gaudí used inverted hanging chains to find the optimal thrust line for arches, then mirrored the result to design the Colònia Güell chapel

MINIMIZE instantaneous single-op J

Gaudí's Hanging Chain Models — dataphys.org

Historical overview of Gaudí's polyfunicular models using weighted strings for the Colònia Güell church

MINIMIZE instantaneous single-op J