Follower force on a filament

A follower force acts along the instantaneous tangent at its point of application. Its direction changes with the filament, making its generalized force nonconservative and allowing oscillatory instabilities in overdamped dynamics.

A two-link follower-force model replaces a filament by two rigid links with torsional springs and point drags. The nonsymmetric linearized stiffness can produce a Hopf bifurcation even without inertia.

The dimensionless follower load compares the moment scale $\Gamma \ell$ of a tangential tip force with a torsional spring constant $k$. In the equal-link two-degree-of-freedom model, straight motion loses stability through a Hopf bifurcation at $\Sigma =3$.