From Constant Impulse Cost to Inertial Amplification: The Complete Energy Framework of the ABÏON Drive.

We present a formal energetic framework for a novel class of propulsion machines based on cyclic momentum transfer through a rotating non-inertial subsystem — herein designated the KVD (Kinetic Vector Drive) / ICV (Impulsor Cinético Vectorial), operating commercially as the ABÏON Drive under the Open-Cycle Constant-Mass Architecture (OCMA). Unlike conventional propulsion systems — whether rocket engines expelling reaction mass or electric motors delivering torque through a shaft — the KVD accelerates a closed working mass centrifugally within a rotating plate, releases it tangentially as pure linear momentum, recovers the kinetic energy via a regenerative electromagnetic damper, and returns the working mass to the cycle center at near-zero relative velocity. No working mass is expelled at any point in the cycle. The central thesis is that conventional energy accounting — equating battery consumption with the vehicle's acquired kinetic energy — constitutes a frame accounting error for this class of machine. It conflates work performed in the moving reference frame of the vehicle with energy measured in the terrestrial inertial frame. These two quantities are not equal, and treating them as equal leads to either apparent violation of energy conservation or systematic underestimation of system efficiency. We derive a formal quantity, the Inertial Amplification Factor Γ, which correctly relates irreversible energy destruction — the true battery cost — to kinetic energy accumulation by the vehicle. The derivation proceeds from first principles: in the vehicle frame, the motor always pays the same energy per impulse ε = ½·m·vₗib² (established in Paper 1, Galilean Invariant Analysis). In the terrestrial frame, the kinetic energy contributed by each impulse grows linearly with vehicle velocity VN, expressed as ΔEₖ^ (N) ≈ m·vₗib·VN. This asymmetry — momentum linear in v, kinetic energy quadratic in v — is the structural source of the system's efficiency advantage. Six formal axioms and four corollaries are proposed to govern energy calculations in KVD / OCMA systems. Axiom I establishes that all sphere energy originates from the battery. Axiom II establishes that the true cost is irreversible energy destroyed, not kinetic energy accumulated. Axiom III establishes constant working mass (dm/dt = 0). Axiom IV establishes frame non-equivalence. Axiom V defines Γ formally. Axiom VI establishes the flywheel optimality principle. Corollaries derive the maximum Γ, the equilibrium velocity Vₑq, cubic thrust scaling, and medium independence. Numerical validation is provided for a reference urban vehicle cycle: M = 1, 000 kg, m = 0. 5 kg, R = 0. 20 m, ω = 2, 500 RPM, vₗib = 52. 4 m/s, f = 83. 3 Hz, ηd = 0. 85, ηc = 0. 904, Vf = 25 m/s (90 km/h). The system achieves Γ = 1. 86, yielding 2. 18× greater kinetic energy per irreversibly consumed Joule compared to a high-efficiency direct-drive electric vehicle (η = 0. 855). Net battery consumption for the complete urban cycle (0 → 90 km/h → 0) is 22. 5 Wh — compared to approximately 150–200 Wh for a conventional EV covering equivalent distance. The analogy to established physical systems is developed in detail: the lever (force amplification at cost of displacement), the heat pump (thermal energy output exceeding electrical input by drawing from ambient reservoir), and the flywheel (stored rotational energy smoothing pulsed demand). In each case, output exceeds actuator input without violating energy conservation — by exploiting a structural asymmetry in how energy is measured across physical domains or reference frames. The KVD exploits the asymmetry between momentum (linear in v) and kinetic energy (quadratic in v) across progressive inertial frames. No physical law is violated. The advantage is architectural. The system's medium independence (Corollary 4) enables qualitatively new applications: propulsion and emergency braking in vacuum, water, ice, or any surface — without requiring grip between vehicle and medium. This capability is absent in all existing propulsion and braking systems. This paper is the third in the five-paper ABÏON Drive Theoretical Foundation Series. It builds directly on Paper 1 (Galilean invariance of energy per impulse) and Paper 2 (constant feeding power at constant thrust) to provide the complete energetic framework connecting impulse cost to vehicle kinetic energy accumulation. Paper 4 extends the framework to full urban cycle accounting and multi-vehicle comparison. Paper 5 generalizes the results to Momentum Engineering and Dynamic Recovery Architectures. Keywords: ABÏON Drive · KVD · Kinetic Vector Drive · ICV · Impulsor Cinético Vectorial · OCMA · Open-Cycle Constant-Mass Architecture · inertial amplification · Inertial Amplification Factor · frame asymmetry · momentum transfer · Galilean invariance · non-inertial frame · rotating mass systems · regenerative propulsion · energy accounting · work-energy theorem · frame non-equivalence · propulsion thermodynamics · medium independence · urban vehicle efficiency · Noether theorem · MIND Theory Series: Paper 3 of 5 — ABÏON Drive Theoretical Foundation Series Related works in this series: Paper 1: Constant-Energy-Per-Impulse Propulsion in the ABÏON Drive: A Galilean-Invariant Analysis. DOI: 10. 5281/zenodo. 20125345 Paper 2: Fixed-Cost Momentum Transfer in the ABÏON Drive. DOI: 10. 5281/zenodo. 20101267 Paper 3: From Constant Impulse Cost to Inertial Amplification: The Complete Energy Framework of the ABÏON Drive. This work. DOI: 10. 5281/zenodo. 20222292 Paper 4: Momentum Engineering and Dynamic Recovery Architectures. DOI: 10. 5281/zenodo. 20222292 Related MIND Theory publications: MIND Theory: Universal Gravitational Spin Generation from Mass Asymmetry. DOI: 10. 5281/zenodo. 18142680 Mechanism of Galaxy Rotation Coherence from Non-Inertial Frame Dragging in General Relativity. DOI: 10. 5281/zenodo. 18211324 License: Creative Commons Attribution 4. 0 International (CC-BY 4. 0)