  Based on a Lie symmetry analysis, we construct a closed form solution to the
kinematic part of the (partial differential) Cosserat equations describing the
mechanical behavior of elastic rods. The solution depends on two arbitrary
analytical vector functions and is analytical everywhere except a certain
domain of the independent variables in which one of the arbitrary vector
functions satisfies a simple explicitly given algebraic relation. As our main
theoretical result, in addition to the construction of the solution, we proof
its generality. Based on this observation, a hybrid semi-analytical solver for
highly viscous two-way coupled fluid-rod problems is developed which allows for
the interactive high-fidelity simulations of flagellated microswimmers as a
result of a substantial reduction of the numerical stiffness.
