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 of a tangential tip force with a torsional spring constant . In the equal-link two-degree-of-freedom model, straight motion loses stability through a Hopf bifurcation at .
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