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A numerical analysis of chaos in the double pendulum

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  • Stachowiak, Tomasz
  • Okada, Toshio

Abstract

We analyse the double pendulum system numerically, using a modified mid-point integrator. Poincaré sections and bifurcation diagrams are constructed for certain, characteristic values of energy. The largest Lyapunov characteristic exponents are also calculated. All three methods confirm the passing of the system from the regular low-energy limit into chaos as energy is increased.

Suggested Citation

  • Stachowiak, Tomasz & Okada, Toshio, 2006. "A numerical analysis of chaos in the double pendulum," Chaos, Solitons & Fractals, Elsevier, vol. 29(2), pages 417-422.
    • Handle: RePEc:eee:chsofr:v:29:y:2006:i:2:p:417-422
    DOI: 10.1016/j.chaos.2005.08.032
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    Cited by:

    1. Chu, Yan-Dong & Chang, Ying-Xiang & Zhang, Jian-Gang & Li, Xian-Feng & An, Xin-Lei, 2009. "Full state hybrid projective synchronization in hyperchaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1502-1510.
    2. Machado, J. A. Tenreiro & Lopes, António M., 2016. "The N-link pendulum: Embedding nonlinear dynamics into the multidimensional scaling method," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 130-138.
    3. An, Xin-Lei & Yu, Jian-Ning & Chu, Yan-Dong & Zhang, Jian-Gang & Zhang, Li, 2009. "Global chaos synchronization of three coupled nonlinear autonomous systems and a novel method of chaos encryption," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 865-873.
    4. Coronel-Escamilla, A. & Gómez-Aguilar, J.F. & López-López, M.G. & Alvarado-Martínez, V.M. & Guerrero-Ramírez, G.V., 2016. "Triple pendulum model involving fractional derivatives with different kernels," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 248-261.
    5. Zhang, Jian-Gang & Li, Xian-Feng & Chu, Yan-Dong & Yu, Jian-Ning & Chang, Ying-Xiang, 2009. "Hopf bifurcations, Lyapunov exponents and control of chaos for a class of centrifugal flywheel governor system," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2150-2168.
    6. Lazare Osmanov & Ramaz Khomeriki, 2022. "Regular and chaotic motion of two bodies swinging on a rod," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(11), pages 1-7, November.
    7. Jiatong Chen & Bin Bao & Jinlong Liu & Yufei Wu & Quan Wang, 2022. "Pendulum Energy Harvesters: A Review," Energies, MDPI, vol. 15(22), pages 1-26, November.
    8. Liu, Zeyi & Rao, Xiaobo & Gao, Jianshe & Ding, Shunliang, 2023. "Non-quantum chirality and periodic islands in the driven double pendulum system," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).

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