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: the canonical three-line resonant signature, the zero-mean-torque native-regime finding, the hybrid motoring-control regime, and matched PMSM baseline comparisons. The saliency sweep (§5.3.2) establishes a three-objective trade space — mean torque, signature amplitude, and conjugate-pair symmetry — as irreducible outputs of a single AC-phase coupling. A new sub-section (§5.3.3) formalises this trade space as a ratio partition: the three outputs map onto the three possible E1P ratio states (E ⇌ 1, E > 1, E < 1), with closure at the Active/Connective balance point, spectra as Active-dominant emission (PM term 32× reluctance at canonical parameters), and remainder as Connective-excess asymmetry. A falsifiable crossover prediction follows: at La1/La0 ≈ 8, the spectra stream transitions from Active-dominant to Connective-dominant, with predicted pair ratio ≈ 0.781, constituting a specific Stage 2.1 testable claim. Topology plates are included for PMDC, PMSM, shape-optimised axial-flux, and field-following lobed resonant-engine geometries. This is Paper I of the first Resonant Systems trilogy.