A geometric framework for dynamics with unilateral constraints and friction, illustrated by an example of self-organized locomotion. (11th April 2018)

• Record Type: Journal Article
• Authors: Ghosh, Shankar; Merin, A. P.; Bhattacharya, S.; Nitsure, Nitin
• Is Part Of: Proceedings. Volume 474:Number 2212(2018)
• Publication Date: 2018-04-11
• Subjects: chirality -- self-organization -- granular matter -- unilateral constraints -- dry friction; Physical sciences -- Periodicals; Engineering -- Periodicals; Mathematics -- Periodicals; 500
• DOI: 10.1098/rspa.2017.0886
• Languages: English
• ISSNs: 1364-5021

Abstract

Abstract : 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.