A geometric framework for dynamics with unilateral constraints and friction.

We present a new 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 behavior 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.

Reference:

Shankar Ghosh, A. P. Merin, Nitin Nitsure: Journal of Physics: Condensed Matter, vol. 29 no. 35 (2017) arXiv:1702.04545

Shankar Ghosh, A. P. Merin, S. Bhattacharya, Nitin Nitsure, arxiv:1605.04438