The oscillation behaviour of a sliding particle under dry friction in a vertical rotating drum is investigated theoretically. A differential equation is set up for general friction laws. For constant friction coefficients, the equation can be solved exactly. For velocity-dependent friction, it can be treated perturbation theoretically. The unperturbed system is solved and with the help of the averaging method, the perturbed system can then be examined for periodic movements. Different structures of the phase space are found for the different friction laws. A friction law given by Rabinowicz reproduces all important aspects of the experiment. Other friction laws are discussed.
Frühjahrstagung der DPG
Deutsche Physikalische Gesellschaft