A Comparative Framework for Extended Classical Mechanics' Frequency-Governed Kinetic Energy

This paper presents a revised formulation of kinetic energy within Extended Classical Mechanics (ECM), interpreting it as a frequency-governed process arising from mass displacement transitions. ECM proposes that kinetic energy emerges from the redistribution of rest mass (Mᴍ) into a dynamic component (ΔMᴍ), structured by two distinct frequency domains: the de Broglie frequency governing translational motion and the Planck frequency reflecting intrinsic quantum excitation. The resulting kinetic energy relation, KEᴇᴄᴍ = (ΔMᴍᵈᴮ + ΔMᴍᴾ)c² = hf, yields the classical ½mv² limit under low-frequency conditions while providing explanatory power for quantum and high-energy phenomena. Applications to atomic transitions, thermionic emission, nuclear fission, and fusion show that observed energy release can be interpreted as frequency-driven mass redistribution rather than annihilation. ECM thus reframes kinetic energy as an emergent property of dual-frequency mass dynamics, offering a unified theoretical lens spanning classical, quantum, and nuclear regimes.