What Is a Catenary?

Catenary refers to a curve, which refers to a uniform (soft and inextensible) chain (thickness and mass distribution) fixed at both ends. The curve shape under the action of gravity, such as suspension bridge It is named because it is similar to the sag of a rope fixed at both ends under the action of uniform gravity. After the coordinate system is properly selected, the equation of the catenary is a hyperbolic cosine function, and its standard equation is: y = a cosh (x / a), where a is the distance from the vertex of the curve to the abscissa axis.

Origin of the problem

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Standard equation

Where a is a constant and is the distance from the vertex of the curve to the abscissa axis. ^[1]

Derivative of hyperbolic sine:

Derivative of hyperbolic cosine:

;

Derivative of inverse hyperbolic sine:

Derivative of inverse hyperbolic cosine: