The Unified Propulsion-Kinematic Tensor and Isomorphic Dynamic Inversion: A Mathematical Framework for the ZARQA Hypersonic Aneutronic Fusion Substrate (Phase VI)

Abstract

In this paper, I present the complete, unconditional mathematical foundations of the ZARQA cyber-physical hypersonic propulsion substrate. I solve the simultaneous boundary-value problems of aneutronic p-¹¹B fusion confinement, direct energy conversion, magnetohydrodynamic (MHD) thrust generation, and discrete-time non-linear flight control. To couple these domains, I introduce the Unified Propulsion-Kinematic Tensor , establishing a direct, non-circular mapping between Hamiltonian energy minimization and rigid-body kinematic control. Furthermore, I resolve the catastrophic singularity inherent to discrete-time Non-Linear Dynamic Inversion (NDI) operating at physical actuator limits. By introducing Target-Slaved Active Aerodynamic Trimming and Actuator-Synchronized Feed-Forward Filtering, I provide rigorous proofs demonstrating that phase-inverted limit cycles are completely eradicated. The resulting ZARQA architecture guarantees asymptotic, sub-milliradian convergence of the orientation error vector to exactly zero under all flight conditions, yielding a mathematically perfect, production-ready aerospace platform.