Chaotic dynamics of a rack-pinion-rack device powered by the Casimir force

Abstract Undesirable effects of chaos suggest the need for a comprehensive understanding of the nonlinear and chaotic behavior of nanodevices powered by the Casimir force. Here, the chaotic dynamics of a nanoscale mechanical device composed of a corrugated cylinder (pinion) placed between two corrugated plates (racks) and coupled via the lateral Casimir force is theoretically and numerically explored when both racks undergo a harmonic lateral motion. Three dimensionless parameters associated with the main observables of the system were identified that fully determine the chaos scenario. We deduced analytical estimates concerning the chaotic threshold in parameter space from the application of Melnikov's method, while some qualitative features of the instability region of equilibria in parameter space are explained with the aid of an energy analysis. Our numerical experiments reasonably confirmed these theoretical predictions and revealed the extreme sensitivity of the nanoscale device to parameter changes as well as different routes order-chaos as the significant parameters are varied.