Contact dynamics
Regarding the sticking case, the friction force is set-valued and determined according to an additional algebraic constraint.
To conclude, the non-smooth approach changes the underlying mathematical structure if required and leads to a proper description of mechanical systems with unilateral contacts and friction.
As a consequence of the changing mathematical structure, impacts can occur, and the time evolutions of the positions and the velocities can not be assumed to be smooth anymore.
In order to handle the changing mathematical structure, the set-valued force laws are commonly written as inequality or inclusion problems.
The approach is associated to the classical DAE theory and leads to robust integration schemes.
The integration of regularized models can be done by standard stiff solvers for ordinary differential equations.
Event-driven integrators distinguish between smooth parts of the motion in which the underlying structure of the differential equations does not change, and in events or so-called switching points at which this structure changes, i.e. time instants at which a unilateral contact closes or a stick slip transition occurs.
At these switching points, the set-valued force (and additional impact) laws are evaluated in order to obtain a new underlying mathematical structure on which the integration can be continued.
In operation, the woodpecker moves down the pole performing some kind of pitching motion, which is controlled by the sleeve.
