Lie Symmetry Analysis of Wave Equation Emanating from Collapse of Shafts in Power Transmission System

Authors

  • George Opiyo Department of Pure and Applied Mathematics, Jaramogi Oginga Odinga University of Science and Technology, Box 210-40601, Bondo-Kenya.
  • Omolo Ongati Department of Pure and Applied Mathematics, Jaramogi Oginga Odinga University of Science and Technology, Box 210-40601, Bondo-Kenya.
  • Aminer Titus Department of Pure and Applied Mathematics, Jaramogi Oginga Odinga University of Science and Technology, Box 210-40601, Bondo-Kenya.
  • Benard Okelo Department of Pure and Applied Mathematics, Jaramogi Oginga Odinga University of Science and Technology, Box 210-40601, Bondo-Kenya.

Keywords:

Integral formulas, Euler-Mascheroni constant, power series expansion, infinite product, Fubini-Tonelli integral theorem, Laplace transform

Abstract

The problematic phenomena of an apparently unintentional beating and the potential collapse of shafts in power transmission systems was discovered by motor ship constructors. In this study, we examine a fourth order Ordinary Differential Equation (ODE), which shows how the collapse of shafts in power transmission networks occurs dynamically. The main focus in this work is to examine and find the solution to the wave equation arising due to collapse of shafts in power transmission systems using Lie symmetry.

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Published

2025-04-14

Issue

Vol. 18 No. 2 (2025): Int. J. Open Problems Compt. Math., Vol. 18, No. 2, June 2025

Section

Articles