A Classical Relativistic Radiation Model of the Hydrogen Atom Electron-Proton Damped Oscillation and Nutation-Induced Emission

This work proposes a classical–relativistic dynamical model of hydrogen atomic radiation based on a non-central electromagnetic interaction between the electron and proton. The hydrogen atom is treated as a relativistically constrained gyroscopic system in which high-speed counter-rotation naturally generates orbital motion and nutation components. By modeling the electron’s nutation motion as a damped oscillator driven by impulsive perturbations, a radiation mechanism is constructed within the framework of classical electrodynamics. The characteristic oscillation frequency derived from this model is shown to be numerically close to the Rydberg frequency associated with hydrogen spectral emission. The analysis integrates relativistic Lorentz factor constraints, orbital energy balance, and a damped oscillator formulation of nutation dynamics. The resulting wave number and frequency scale are compared directly with the Rydberg constant. This work does not aim to replace the quantum-mechanical description of the hydrogen atom. Instead, it provides a classical–relativistic reinterpretation of atomic radiation phenomena and proposes a mechanism-level explanation for the emergence of the Rydberg frequency from electron–proton dynamics.