A New Interpretation Framework Based on Variational Principles for Non-Collision Trajectory Deformation

A New Interpretation Framework Based on Variational Principles for Non-Collision Trajectory Deformation Jae Un Kim1 1Independent Researcher, Seoul, Korea [email protected] Abstract This study proposes a framework for integrating and analyzing the deformation of trajectories caused by non-collision interactions into a formula based on the principle of variance. Existing trajectory analysis methods have been approached independently depending on each interaction or physical system, and trajectory equations have tended to be determined separately depending on the type of force. In comparison, this study starts from the perspective of the principle of minimum action, derives a **single trajectory equation (CORE)** and expresses all interactions as one potential function V(r), thereby achieving integration by analyzing trajectory changes regardless of the type and form of interactions through the formula. This method has the scalability to handle all non-collision interactions such as gravity, electromagnetic force, relativistic correction terms, and multiple potentials within a single mathematical structure. 1 Introduction The problem of trajectory in physics has been dealt with for a long time in an individual and local way. It has been analyzed separately for each individual interaction, such as the gravitational trajectory problem under Newtonian mechanics, the Lorentz trajectory under electromagnetic force, or the precession problem in a calibrated trajectory, and in this process, the fundamental structural unity of the trajectory has not been fully explored. However, the trajectory is essentially **”optimized path”**, which is directly related to the area covered by the variational method. Therefore, if we reconstruct the trajectory problem into an integrated formula system based on the principle of minimum action, we can build a framework that can analyze all trajectory variants into a single logic beyond simply listing the types of forces or solving them on a case-by-case basis. 2 Conclusion Neith provides a structured explanation for second-order gravitational responses, offering a field-based alternative to dark matter. It functions as a deterministic vector field shaped by 1 the geometry of spacetime itself under SRE, and opens new pathways for relativistic field engineering. 2