Dynamic Analysis and Stability Evaluation of a Discrete Mathematical Model for Flying Fox String Vibrations

  • Aniq Nur Matsubah Universitas Islam Negeri Maulana Malik Ibrahim
  • Ali Hussein Al-Moders Iraqi Ministry of Education
  • Francis Pantino West Visayas State University
  • Asgar Anda Mindanao State University
DOI: https://doi.org/10.37251/ijome.v3i1.1576
Keywords: Dynamic Analysis, Discrete Flying Fox Model, String Deflection, String Deflection Angle

Abstract

Purpose of the study: This study aims to find the stability of changes in string deflection and the angle of string deflection when an object is launched along a flying fox.

Methodology:This study uses a model developed by Kusumastuti et al. (2017). There are two models analyzed, namely the discrete model of the string deviation y(t) and the angle of the string deviation θ(t). The analysis steps include model reduction, model discretization, model linearization, fixed point search, and stability analysis. Stability is analyzed based on the eigenvalues ​​it has.

Main Findings:Based on the research conducted, the following eigenvalues ​​were obtained: λ1 = -0.005h + (0.14565h)i, λ2 = -0.005h - (0.14565h)i, λ3 = -0.005h + (0.1331480769h)i, and λ4 = -0.005h - (0.1331480769h)i. The results of the study indicate that the system is in a stable condition (sink) because all eigenvalues ​​obtained are complex numbers with negative real parts. Thus, it can be concluded that the rope deflection, rope deflection velocity, rope deflection angle, and rope deflection angular velocity are in a stable condition.

Novelty/Originality of this study: This study provides a new contribution to the understanding of discrete system dynamics in flying fox string vibrations, by showing that the stability of the system can be analyzed through the negative complex eigenvalues ​​generated from the model.

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Published
2025-05-02
How to Cite
Matsubah, A. N., Al-Moders, A. H., Pantino, F., & Anda, A. (2025). Dynamic Analysis and Stability Evaluation of a Discrete Mathematical Model for Flying Fox String Vibrations. Interval: Indonesian Journal of Mathematical Education, 3(1), 35-44. https://doi.org/10.37251/ijome.v3i1.1576
Issue
Vol. 3 No. 1 (2025): June
Section
Articles

Copyright (c) 2025 Aniq Nur Matsubah, Ali Hussein Al-Moders, Francis Pantino, Asgar Anda

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