ABÏON PRIME The Dynamic-State Energy Relation

Abstract

ABÏON PRIME introduces an engineering framework for analyzing momentum transfer within a progressively increasing dynamic state of a rotating mechanical system. Starting from the classical definitions of linear momentum and kinetic energy, the work derives the finite momentum–energy relation ΔK = v·Δp + (Δp)²/(2M), showing that the kinetic-energy consequence of a given momentum increment depends explicitly on the instantaneous velocity of the receiving mass. The differential form dK = v·dp provides a compact description of this state dependence and is extended to rotational systems through the tangential velocity relation V = ωR. ABÏON PRIME proposes an architecture in which approximately controlled momentum increments are repeatedly delivered to a flywheel at progressively higher tangential velocities, while the working masses remain dynamically integrated within the system and are subsequently recovered. A discrete event-by-event mathematical model is developed to describe momentum transfer, angular-momentum accumulation, flywheel angular velocity, kinetic-energy evolution, actuator energy expenditure, regenerative recovery, losses, and cumulative gain. Under the idealized constant-parameter model, angular velocity evolves linearly with the number of momentum-transfer events, while the associated flywheel kinetic energy follows a quadratic dependence on event number. The study distinguishes event-level kinetic-energy amplification from net system-level energy generation and defines the experimental conditions required to discriminate between these two phenomena through complete energy accounting. PRIME is therefore presented not as a modification of classical mechanics, but as an experimentally testable architectural hypothesis concerning the systematic organization of momentum transfer within a closed rotating mechanical system. KEYWORDS: ABÏON PRIME; momentum transfer; kinetic energy; dynamic state; momentum–energy relation; rotational dynamics; angular momentum; flywheel; tangential velocity; momentum architecture; Momentonics; regenerative recovery; energy accounting; mechanical systems; experimental falsifiability.