RT Journal Article
SR Electronic
T1 A geometric framework for dynamics with unilateral constraints and friction, illustrated by an example of self-organized locomotion
JF Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science
FD The Royal Society
DO 10.1098/rspa.2017.0886
VO 474
IS 2212
A1 Ghosh, Shankar
A1 Merin, A. P.
A1 Bhattacharya, S.
A1 Nitsure, Nitin
YR 2018
UL http://rspa.royalsocietypublishing.org/content/474/2212/20170886.abstract
AB 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.