TITLE:
A Simulated Unified Resultant Amplitude Method for Multi-Dimensional/Multi-Variable Opposite Wave Summation
AUTHORS:
Shawn P. Guillory
KEYWORDS:
Waves, Resultant Amplitude, Euler’s Equation, Unified Theory, Spectral Analysis, Kinematics
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.13 No.1,
January
26,
2025
ABSTRACT: The simulated unified resultant amplitude theory studies function and polar graphs of sinusoidal radial waves including the cosine, sine, and summation waves for determining separate combination-wave equations arising from 2D spatial oscillator fields in each of the four quadrants corresponding to the x-y Cartesian reference frame. Combination-wave fluctuations in terms of their algebraic signs are then extrapolated and mathematically modeled relative to the quadrant number by way of Euler’s equation. The resulting sign fluctuation equations are used to synthesize the combination-wave equations into a single unified equation along with a unified wave rotation solution that adequately represents all four quadrant-specific wave equations. Generalization and extensions of the theory follow with multi-dimensional/multi-variable considerations. Subsequently, utilization of the theory regarding an applied mathematics and physics-based kinematics motion problem, a generalized differential equation solution for a spring system, as well as a four-dimensional/four-variable dual-cone example are provided for validating the methodology. Consequently, it is shown that the proposed unified model is useful for performing a compact resultant amplitude analysis within general applications involving various wave phenomena.