Dynamic Analysis and Stability Evaluation of a Discrete Mathematical Model for Flying Fox String Vibrations - Matsubah, Aniq Nur; Al-Moders, Ali Hussein; Pantino, Francis; Anda, Asgar (jurnal matematika, 2025)
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.