  It is well known that a straight Nambu-Goto string is an exact solution of
the equations of motion when its end moves in a circular orbit. In this paper
we investigate the shape of a confining relativistic string for a general
motion of its end. We determine analytically the shape of the curved string to
leading order in deviation from straightness, and show that it reduces to an
expected non-relativistic result. We also demonstrate numerically that in
realistic meson models this deviation is always small. We further find that the
angular momentum and energy are the same as for the straight string, but that
the curved string has a small radial momentum not present in a straight string.
Our results justify the common assumption of straight strings usually made in
hadron models.
