Diffusion-governed dynamical system for Coulombic rolling of cylinders bent by normal flux

Chen Xuan

Chaos, Solitons & Fractals, 2026, vol. 209, issue P1

Abstract: This paper systematically analyzes a minimal differential–algebraic equation (DAE) model for the Coulombic rolling of flux-bent cylinders. Operating in the limit of negligible inertia, the system couples exponential curvature relaxation via diffusion with rotation-induced advection, constrained by a dry friction balance that mathematically links curvatures to rolling velocity. Based on an irreducible dimensionless system dependent on a single flux ratio q/qc, I classify regimes of motion based on algebraic admissibility and physical viability, revealing inherent impasse singularities and parasitic solution branches. Bifurcation and stability analysis establishes a critical flux |q|=qc (determined by rolling friction as well as cylinder properties) for a saddle–node bifurcation that yields stable and unstable steady rolling states jumping discontinuously from a stationary state. Furthermore, I identify a second threshold |q|/qc=4/33/4 that fundamentally reconfigures the phase space topology. This second threshold reshapes the admissible manifolds, rewires branch connectivity, and flips the stability of fixed points by altering the reduced one-dimensional dynamics. Finally, I highlight the structural limitations of the disjoint constraint manifolds, emphasizing the need for future branch-transition mechanisms to fully resolve onset and cessation events.

Keywords: Diffusion; Bifurcation; Soft robotics; Rolling friction (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:209:y:2026:i:p1:s0960077926005436

DOI: 10.1016/j.chaos.2026.118402

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