  In this paper we explore a numerical scheme for a nonlinear fourth order
system of partial differential algebraic equations that describes the dynamics
of slender inextensible elastica as they arise in the technical textile
industry. Applying a semi-discretization in time, the resulting sequence of
nonlinear elliptic systems with the algebraic constraint for the local length
preservation is reformulated as constrained optimization problems in a Hilbert
space setting that admit a solution at each time level. Stability and
convergence of the scheme are proved. The numerical realization is based on a
finite element discretization in space. The simulation results confirm the
analytically predicted properties of the scheme.
