Mechanical Dynamics

This monograph establishes a rigorous mechanical framework that reinterprets classical dynamics, relativistic phenomena, and cosmological anomalies through first-principles particle matrix interactions. By substituting abstract geometric curvatures and unobserved entities with concrete spatial pressure gradients, volumetric containment$(V)$, and matrix residence durations $(t_{\text{res}})$, the $n^3$ framework offers a unified mechanical foundation for physical systems across micro and macro scales. Key contributions include the formulation of a master power-balancing equation uniting dynamic environmental drag, capacity saturation $(C_{\text{sat}})$, thermal leakages, and threshold-triggered acoustic and shock dissipation, effectively resolving mathematical singularities through physical boundaries. Furthermore, the work successfully derives mechanical solutions for astrophysical anomalies—such as Pioneer spacecraft deceleration, flat galactic rotation curves without dark matter, planetary flyby anomalies, and solar coronal $heating—while$ introducing hierarchical matrix dynamics and bounded deterministic evolution.