10.6084/m9.figshare.6022283.v1 Shankar Ghosh Shankar Ghosh A. P. Merin A. P. Merin S. Bhattacharya S. Bhattacharya Nitin Nitsure Nitin Nitsure Supplementary Information from A geometric framework for dynamics with unilateral constraints and friction, illustrated by an example of self-organized locomotion The Royal Society 2018 chirality self-organization granular matter unilateral constraints dry friction 2018-03-23 14:14:44 Journal contribution https://rs.figshare.com/articles/journal_contribution/Supplementary_Information_from_A_geometric_framework_for_dynamics_with_unilateral_constraints_and_friction_illustrated_by_an_example_of_self-organized_locomotion/6022283 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.