Mathematical Analysis of TDI a New Rotational Mechanic

Abstract

An alternative conceptual framework has been developed for the analysis of systems with intrinsic rotation, even when subjected to non-coaxial interactions, in accordance with the Theory of Dynamic Interactions (TDI).

Figure 1. Cover of the book New Celestial Mechanics

In the book by the same authors, New Celestial Mechanics (NCM), which has been published, this theory is analyzed and described, having been studied for more than four decades. The proposed approach does not seek to replace the classical mechanics of Kepler, Newton or Euler, but rather to expand its conceptual domain in regimes where intrinsic rotation, precession, and the geometric sequence of interactions play a dynamically relevant role.

Rotation–translation coupling is discussed as an organizing hypothesis capable of inducing closed trajectories and dynamic equilibrium states of the center of mass without necessarily resorting, as a primary postulate, to an explicit centripetal force in its usual formulation.

To confirm the theory, various experimental prototypes were developed by the Advanced Dynamics / Dinámica Fundación team, whose observations are compatible with the proposed framework and could motivate new experimental and numerical investigations.

In its mathematical analysis, the Theory of Dynamic Interactions (TDI) is not formulated as a single closed equation, but as an alternative mathematical–physical framework to classical mechanics for describing systems with intrinsic rotation, subjected to excitations that would generate simultaneous non-coaxial rotations. Its structure is built in overlapping layers, in a coherent and causal way.