Profile of a rotating string

The problem of a uniform flexible chain or string rotating about an axis with fixed ends is addressed in the context of both Newtonian mechanics and the variational principle. It is shown that, in the absence of gravity, the equations describing the profile of the string as well as the constraints of the system are all expressible in terms of Legendreʹs elliptic integrals of various kinds. The effect of gravity is discussed qualitatively, and it is shown that for high enough angular velocities its effect is negligible. The profile of a rotating chain is obtained using stroboscopic photography and compared with the theoretical results.