English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We report on the motion of a spinning sleeping top on an inclined plane.Below a critical inclination angle the sleeping tops are force free. Thetrajectory of a sleeping top on weakly inclined planes in the adiabatic limitis invariant of the angular frequency of the top and thus invariant under arescaling of the time, however not invariant under time reversal. Thestationary trajectory of the sleeping top is characterized by its angle to thein plane horizontal direction. At larger inclinations of the plane thestationary motion of the top becomes unstable and the top accelerates downhill.The behavior points towards a complex law of dry friction of the contact pointbetween the top tip and the material of the inclined plane that depends on aslip parameter. We propose a phenomenological law of dry friction that canexplain the relaxation of the top into the sleeping position, the geometricbehavior of the top trajectories, and the instability of the stationary motionat larger inclination angles.

The geometric phase and the dry friction of sleeping tops on inclined planes