  This contribution provides a general framework to use Lagrange multipliers
for the simulation of low Reynolds number fiber dynamics based on Bead Models
(BM). This formalism provides an efficient method to account for kinematic
constraints. We illustrate, with several examples, to which extent the proposed
formulation offers a flexible and versatile framework for the quantitative
modeling of flexible fibers deformation and rotation in shear flow, the
dynamics of actuated filaments and the propulsion of active swimmers.
Furthermore, a new contact model called Gears Model is proposed and
successfully tested. It avoids the use of numerical artifices such as repulsive
forces between adjacent beads, a source of numerical difficulties in the
temporal integration of previous Bead Models.
