The motion of a sliding particle, influenced by friction, in a rotating drum is investigated. A differential equation is formulated for general friction laws. Assuming a constant coefficient of friction, the equation is exactly solvable. For a velocity dependent coefficient of friction, perturbation methods may be used. The nonperturbed system is solved and with the help of the averaging method, the perturbed system can be examined for periodic motions. Different friction laws lead to qualitatively different behaviours, including a stable fixed point in the phase plot, marginally stable orbits and stable limit cycle behaviour. A friction law proposed by E. Rabinowicz reproduces the major result of the experiment, i.e., convergence towards a limit cycle. Other laws will be discussed.
Friction, Arching, Contact Dynamics, pages 305-309, World Scientific