0
$\begingroup$

I have two points in 3D space, A and B. I need to have a parametric equation of the catenary curve such that:

Cat(0) = A,

Cat(1) = B,

Cat(t)= f(t, A, B)

How can I derive the function f

$\endgroup$

1 Answer 1

2
$\begingroup$

The catenary is known to follow the equation

$$y=a\left(\cosh\left(\frac{x-x_0}a\right)-1\right)+y_0$$ in 2D, where $a, x_0$ and $y_0$ are adjustable parameters.

You need to change the coordinates to work in the vertical plane that contains $A$ and $B$, and you also need a third piece of information to determine the parameters, such as the length of the curve.

Unfortunately, due to the transcendental nature of the equations, only a numerical resolution is possible.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.