Revealing the Structure of Motion Dynamics Through Spatial-Energy Parameterization

This paper examines the transition from the traditional temporal parameterization of classical mechanics to a spatial-energy interpretation within the framework of the Deterministic Theory of Mechanics (DTM). It is shown that Newton’s second law admits an equivalent spatial-energy form: 𝐹 𝑑𝑠=𝑚𝑣 𝑑𝑣 The paper introduces the concept of the inertia level of a system: 𝐼=𝑚𝑣 and formulates the law of spatial change of the state of motion: 𝜒(𝑠)=𝐹𝐼(𝑠)According to DTM, motion is interpreted not merely as a temporal process but as a continuous causal-energy transformation of the dynamical state of a system. It is shown that as velocity increases, the inertia level of the system also increases, leading to a reduction in the spatial rate of change of the state of motion and to a nonlinear growth of energy expenditure required for further acceleration. The proposed approach preserves full mathematical compatibility with classical mechanics while extending its causal-energy interpretation.