In this note we introduce a hierarchy of phase spaces for static friction, which give a graphical way to systematically quantify the directional dependence in static friction via subregions of the phase spaces. We experimentally plot these subregions to obtain phenomenological descriptions for static friction in various examples where the macroscopic shape of the object affects the frictional response. The phase spaces have the universal property that for any experiment in which a given object is put on a substrate fashioned from a chosen material with a specified nature of contact, the frictional behaviour can be read off from a uniquely determined classifying map on the control space of the experiment which takes values in the appropriate phase space.

We present a geometric framework to deal with mechanical systems which have unilateral constraints, and are subject to damping/friction, which cannot be treated within usual classical mechanics. In this new framework, the dynamical evolution of the system takes place on a multidimensional curvilinear polyhedron, and energetics near the corners of the polyhedron leads to qualitative behaviour such as stable entrapment and bifurcation. We illustrate this by an experiment in which dumbbells, placed inside a tilted hollow cylindrical drum that rotates slowly around its axis, climb uphill by forming dynamically stable pairs, seemingly against the pull of gravity.

No abstract