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The N-link pendulum: Embedding nonlinear dynamics into the multidimensional scaling method

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  • Machado, J. A. Tenreiro
  • Lopes, António M.

Abstract

This paper explores the use of multidimensional scaling for analyzing the dynamics of the N-link planar pendulum. Several integer- and fractional-order pendular systems are studied based on the time response and energy of the links. The dynamics get increasingly complex and chaotic with the number of degrees-of-freedom. The numerical experiments demonstrate the feasibility of the proposed methodology in analyzing the data and motivate its extension for other performance measures and dynamical systems.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:89:y:2016:i:c:p:130-138
    DOI: 10.1016/j.chaos.2015.10.013
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    References listed on IDEAS

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    1. Nigmatullin, Raul R. & Omay, Tolga & Baleanu, Dumitru, 2010. "On fractional filtering versus conventional filtering in economics," MPRA Paper 111643, University Library of Munich, Germany.
    2. J. Kruskal, 1964. "Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis," Psychometrika, Springer;The Psychometric Society, vol. 29(1), pages 1-27, March.
    3. Tolga Omay & Dumitru Baleanu, 2009. "Solving Technological Change Model by Using Fractional Calculus," International Studies in Entrepreneurship, in: Neslihan Aydogan (ed.), Innovation Policies, Business Creation and Economic Development, chapter 1, pages 3-12, Springer.
    4. JA Tenreiro Machado & Maria Eugénia Mata, 2015. "Analysis of World Economic Variables Using Multidimensional Scaling," PLOS ONE, Public Library of Science, vol. 10(3), pages 1-17, March.
    5. Stachowiak, Tomasz & Okada, Toshio, 2006. "A numerical analysis of chaos in the double pendulum," Chaos, Solitons & Fractals, Elsevier, vol. 29(2), pages 417-422.
    6. Edmundo Capelas de Oliveira & José António Tenreiro Machado, 2014. "A Review of Definitions for Fractional Derivatives and Integral," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-6, June.
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    Cited by:

    1. Jose Tenreiro Machado & Alexandra M. Galhano & Carla S. Cordeiro, 2021. "Discretization of Fractional Operators: Analysis by Means of Advanced Computational Techniques," Mathematics, MDPI, vol. 9(19), pages 1-16, September.

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