Induced Kinetic Energy and Polarization of Particle Motion

IMPORTANT UPDATE: This version is incomplete. Please refer to Version 2 for the full research paper, including all simulations, case studies, and complete data analysis. You can find the latest version here: https://doi.org/10.5281/zenodo.18958186 The analysis of Induced Kinetic Energy (IKE) represents an innovative approach for studying internal motion phenomena in materials subjected to dynamic excitation, particularly in seismic events and complex mechanical systems. The principle introduced here considers the angular distribution of kinetic energy as a fundamental parameter for describing both the local and global response of a material point during induced motion. This formulation allows the direction and intensity of energy propagation to be evaluated, providing a more realistic three-dimensional representation than traditional models based only on scalar or vector components. In this work we present: the theoretical foundations of IKE, the simulation methodology, and the results obtained from synthetic signals generated in the North, East and Vertical directions. The data processing allowed the induced energy fields to be represented both in two-dimensional polar form and in three-dimensional angular surfaces. Preliminary results show a clear correlation between the angular distribution of induced kinetic energy and the local dynamics of the system, highlighting the potential of the method as a tool for investigating induced motion and predictive modelling of energetic behaviour.