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

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