Resonant Engines

This preprint organizes a research program for developing a new rotary electromagnetic machine termed a resonant engine. The candidate machine combines a permanent-magnet-biased rotor, superposed stator winding sets that realize distinct magnetic-circuit roles, and a resonant converter/control stack intended to alternate between those roles near half the mechanical rotation frequency. Energetic First Principles (E1P) is used as a design-generating framework. The paper defines the candidate architecture, states the engineering hypotheses, distinguishes architectural identity from control regimes, specifies observables and comparison baselines, and lays out a development program with decision gates. The paper includes symbolic and numerical Stage 1/Stage 2 results, including the canonical three-line resonant signature, the zero-mean-torque native-regime finding, the hybrid motoring-control regime, and matched PMSM baseline comparisons. It also includes topology plates for PMDC, PMSM, shape-optimised axial-flux, and field-following lobed resonant-engine geometries. This is Paper I of the first Resonant Systems trilogy.