Euler-Kirchhoff filaments are solutions of the static Kirchhoff equations f
or elastic rods with circular cross sections. These equations are known to
be formally equivalent to the Euler equations for spinning tops. This equiv
alence is used to provide a classification of the different shapes a filame
nt can assume. Explicit formulas for the different possible configurations
and specific results for interesting particular cases are given. In particu
lar, conditions for which the filament has points of self-intersection, sel
f-tangency, vanishing curvature or when it is closed or localized in space
are provided. The average properties of generic filaments are also studied.
They are shown to be equivalent to helical filaments on long length scales
. (C) 1999 American Institute of Physics. [S0022-2488(99)05006-9].