# From where the so-named “elastica problem” is coming from?

In a book by Cash et al, I see the mention of the so-called Elastica problem (pg 221 in the link here).

The problem is presented as a system of ODEs,

$$x' = \cos (\phi)$$

$$y' = \sin (\phi)$$

$$\phi' = \kappa$$

$$\kappa' = F \cos (\phi)$$

and when I looked for where these ODEs come from I could not find a clear derivation anywhere. There are references to Bernoulli, Euler, but the formulation looked different. Does anyone know a book, reference that shows where these equations come from?

Thanks,

• Reviewers: likely proof that the question is on-topic. – peterh - Reinstate Monica Aug 30 '19 at 20:34
• So $\kappa'$ is just $x'$ times a constant, or is $F$ a function? – Carl Witthoft Sep 3 '19 at 13:36