Minima for Elastics on Rigid Cylinders
Vagn Lundsgaard Hansen · SIAM Review · 1989
The theory of global calculus of variations in nonlinear spaces of maps is illustrated in the simple case of maps of the circle into itself. As an application, the behaviour of an elastic on a frictionless rigid cylinder is explained by identifying the well-known equilibrium positions of the elastic as the minima for a suitable energy function on the space of all smooth maps of the circle into itself.