Instability of Ostrogradsky Formalism and Stability Conditions in Non-Inertial Physics

This preprint presents a stability-based approach to higher-derivative dynamics in non-inertial reference frames. By imposing the non-negativity of the second variation of the action, a dynamically admissible subset of trajectories is selected within the Ostrogradsky formalism. The resulting extended Hamilton–Jacobi structure naturally contains an additional term that coincides with the Bohm quantum potential in the Madelung representation of the Schrödinger equation. The work is related to the author’s contribution to the BSM 2025 conference and is shared here to ensure early dissemination of the results.