Foundational Formulation of Extended Classical Mechanics: From Classical Force Laws to Relativistic Dynamics

This research develops the foundational equations of Extended Classical Mechanics (ECM) by generalizing Newtonian mechanics through the inclusion of dynamic mass components such as negative apparent mass. ECM redefines force, acceleration, and gravitational interactions using an effective mass framework, expressed as the sum of traditional matter mass and a kinetic-energy-derived negative apparent mass. This dual-mass interaction leads to revised force laws and a spectrum of speed regimes for massive particles—ranging from gravitational confinement to antigravitational liberation. The formulation extends to massless particles like photons by assigning them an effective negative matter mass, enabling consistent force definitions and propagation behaviour at relativistic speeds. Radial distance plays a critical role in determining gravitational behaviour, with transitions from classical attraction to antigravitational expansion. The framework aligns with cosmological observations, particularly in large-scale structure behaviour, and provides a unified approach to understanding force, inertia, and motion in both massive and massless domains. ECM thus represents a coherent advancement of classical physics, accommodating gravitational variance, energy redistribution, and speed constraints in dynamic systems.