So I'm having such a problem:
There is given parametric curve, let's call it L. The curve is then slightly deformed so that there are perpendicular defomations given by the function g(s) along the L. What I need is the difference in curvature between deformed and undeformed state of the curve. Will this be simply the curvature of the function g(s), which then, under assumption of small deformations, could be approximated by its 2nd derivative?
The problem, simplifying a bit, is about calculating the elastic energy of deformed curved beam.