Stability-Classical Discreteness in the Hydrogen Atom: Non-Inertial Dynamics with Higher-Order Time Derivatives

A classical dynamical framework with higher-order time derivatives is developed in which discrete atomic spectra emerge as a consequence of stability conditions rather than quantum postulates. Physical states are associated with dynamically stable regimes in an extended configuration space. A harmonic representation of classical dynamics introduces an action scale Y, whose minimal admissible value is selected by stability. The hydrogen atom is analyzed as a representative system, yielding the standard energy spectrum at leading order and characteristic higher-order corrections. Non-inertial contributions are formulated consistently at the level of the action. Possible experimental implications are briefly discussed.