Rings of same gravity center

Question

Using calculus of variations or otherwise, how do we find all non-circular ovals of loop length $ 2\pi $ in the plane with its center of gravity of arc at $ (0,0)? $

By oval, do you mean ellipse or something more generic? – Semiclassical Jun 09 '16 at 19:36 — Semiclassical, Jun 09 '16 at 19:36

score 1 · Accepted Answer · answered Jun 09 '16 at 19:41

1

If by "oval" you mean something relatively general such as a smooth convex closed curve, there is a large supply of those meeting the conditions. Any curve symmetric around $(0,0)$ with the given perimeter would work.

answered Jun 09 '16 at 19:41

zyx

35,436

Was in error :( , wanted to say something else.. – Narasimham Jun 09 '16 at 21:40

Rings of same gravity center

1 Answers1