Applied Electromagnetics

Applied Electromagnetics

Numerical study of the effect of initial conditions on the behavior of a double physical pendulum

Document Type : Original Article

Authors
Abdol Jabbar Shokri 1
Behrooz Malek-Alkalmi 2
1 Assistant Professor, Payam Noor University, Sanandaj, Iran
2 Associate Professor, University of Kurdistan, Sanandaj, Iran
Abstract
The double physical pendulum serves as a mechanical model that effectively demonstrates the complex phenomena of nonlinear dynamic systems, including chaotic behavior. In this study, using the finite element method (FEM) and numerical simulations, the high sensitivity of the system’s behavior to initial conditions has been investigated. The results show that changes in initial parameters such as the angle of deviation, length, and mass of the outer pendulum can lead to unpredictable and complex trajectories. For a more detailed analysis, first, a mathematical model for the double physical pendulum was created using Lagrangian mechanics. Then, using numerical calculations and analytical tools such as Fast Fourier Transform (FFT) and Poincaré surface, the effect of changing initial conditions was comprehensively studied. The results showed that increasing the initial deviation angle of the outer pendulum at different values (12, 30, 60, 88, 92, and 128 degrees), as well as increasing the mass and length of the second connecting rod, causes the system’s behavior to change from periodic to quasi-periodic and chaotic states. These findings emphasize the importance of initial conditions in predicting the behavior of nonlinear systems and provide valuable insights in the field of nonlinear dynamics.
Keywords
Double pendulum
initial conditions
simulation
Poincaré surface
fast Fourier transform
chaos

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Applied Electromagnetics
Volume 13, Issue 2 - Serial Number 31
Autumn and Winter
February 2026
Pages 1-15

  • Receive Date 25 August 2025
  • Revise Date 29 September 2025
  • Accept Date 17 October 2025
  • Publish Date 02 November 2025