In the framework of classical noninertial mechanics, the theoretical construction is predicated on the existence of a special reference frame, the "inertial frame", as a priori. Its essence is to extend the dynamical laws in the inertial frame to noninertial frames through coordinate transformation and formal modification, thus inherently relying on the definition and existence of the inertial frame, making it difficult to achieve a fundamental breakthrough in the inertial frame paradigm. This paper proposes a dynamic reconstruction path based on the intrinsic relations within the system, aiming to establish a new system of particle dynamics that is logically self-consistent and physically self-sufficient and does not presuppose an absolute space-time background. On the basis of Newton's laws of motion, in this paper, the equations of particle mechanics applicable to any translational reference frame (i.e., a reference frame with an origin acceleration that can be any function of time) are derived. Through systematic analysis, it is proven that core physical quantities such as force, momentum, and the kinetic energy of a particle group all possess intrinsic properties independent of the choice of reference frame. By further introducing a particle subsystem grouping mechanism, this paper reveals the dynamical essence of internal interactions within the system and its coupling with the external environment, clarifying the physical origin of the energy hierarchy structure (internal kinetic energy and external kinetic energy) and its conservation conditions in general reference frames, thereby providing a solid theoretical foundation and an operational, verifiable mathematical framework for constructing a truly universal noninertial mechanics theory that does not require the introduction of fictitious inertial forces.