In this article we propose a novel geometric model to study the motion of a
physical flag. In our approach a flag is viewed as an isometric immersion from
the square with values into R3 satisfying certain boundary
conditions at the flag pole. Under additional regularity constraints we show
that the space of all such flags carries the structure of an infinite
dimensional manifold and can be viewed as a submanifold of the space of all
immersions. The submanifold result is then used to derive the equations of
motion, after equipping the space of isometric immersions with its natural
kinetic energy. This approach can be viewed in a similar spirit as Arnold's
geometric picture for the motion of an incompressible fluid.Comment: 25 pages, 1 figur