%0 Journal Article
%T A Simulated Unified Resultant Amplitude Method for Multi-Dimensional/Multi-Variable Opposite Wave Summation
%A Shawn P. Guillory
%J Journal of Applied Mathematics and Physics
%P 281-301
%@ 2327-4379
%D 2025
%I Scientific Research Publishing
%R 10.4236/jamp.2025.131013
%X 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 <i>x</i>-<i>y</i> 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&#8217;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.
%K Waves
%K Resultant Amplitude
%K Euler&#8217
%K s Equation
%K Unified Theory
%K Spectral Analysis
%K Kinematics
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=140205