IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v89y2016icp130-138.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077915003239
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2015.10.013?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Stachowiak, Tomasz & Okada, Toshio, 2006. "A numerical analysis of chaos in the double pendulum," Chaos, Solitons & Fractals, Elsevier, vol. 29(2), pages 417-422.
    4. Nigmatullin, Raul R. & Omay, Tolga & Baleanu, Dumitru, 2010. "On fractional filtering versus conventional filtering in economics," MPRA Paper 111643, University Library of Munich, Germany.
    5. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Roger Shepard, 1974. "Representation of structure in similarity data: Problems and prospects," Psychometrika, Springer;The Psychometric Society, vol. 39(4), pages 373-421, December.
    2. Giovanna Boccuzzo & Licia Maron, 2017. "Proposal of a composite indicator of job quality based on a measure of weighted distances," Quality & Quantity: International Journal of Methodology, Springer, vol. 51(5), pages 2357-2374, September.
    3. Ma, Jie & Tse, Ying Kei & Wang, Xiaojun & Zhang, Minhao, 2019. "Examining customer perception and behaviour through social media research – An empirical study of the United Airlines overbooking crisis," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 127(C), pages 192-205.
    4. Muñoz-Mas, Rafael & Vezza, Paolo & Alcaraz-Hernández, Juan Diego & Martínez-Capel, Francisco, 2016. "Risk of invasion predicted with support vector machines: A case study on northern pike (Esox Lucius, L.) and bleak (Alburnus alburnus, L.)," Ecological Modelling, Elsevier, vol. 342(C), pages 123-134.
    5. Ivan Mihál & Eva Luptáková & Martin Pavlík, 2021. "Wood-inhabiting macromycete communities in spruce stands on former agricultural land," Journal of Forest Science, Czech Academy of Agricultural Sciences, vol. 67(2), pages 51-65.
    6. Marie Diekmann & Ludwig Theuvsen, 2019. "Value structures determining community supported agriculture: insights from Germany," Agriculture and Human Values, Springer;The Agriculture, Food, & Human Values Society (AFHVS), vol. 36(4), pages 733-746, December.
    7. D. V. Pahan Prasada, 2013. "Domestic versus Multilateral Institutions in Bilateral Trade: A Comparative Gravity Analysis," International Economic Journal, Taylor & Francis Journals, vol. 27(1), pages 127-142, March.
    8. Malcolm Dow & Peter Willett & Roderick McDonald & Belver Griffith & Michael Greenacre & Peter Bryant & Daniel Wartenberg & Ove Frank, 1987. "Book reviews," Journal of Classification, Springer;The Classification Society, vol. 4(2), pages 245-278, September.
    9. Mark Davison, 1988. "A reformulation of the general Euclidean model for the external analysis of preference data," Psychometrika, Springer;The Psychometric Society, vol. 53(3), pages 305-320, September.
    10. Enrico di Bella & Matteo Corsi & Lucia Leporatti, 2015. "A Multi-indicator Approach for Smart Security Policy Making," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 122(3), pages 653-675, July.
    11. Willem Heiser, 1991. "A generalized majorization method for least souares multidimensional scaling of pseudodistances that may be negative," Psychometrika, Springer;The Psychometric Society, vol. 56(1), pages 7-27, March.
    12. Pietro Lovaglio & Mario Mezzanzanica, 2013. "Classification of longitudinal career paths," Quality & Quantity: International Journal of Methodology, Springer, vol. 47(2), pages 989-1008, February.
    13. Geert Soete & Willem Heiser, 1993. "A latent class unfolding model for analyzing single stimulus preference ratings," Psychometrika, Springer;The Psychometric Society, vol. 58(4), pages 545-565, December.
    14. Luís Francisco Aguiar & Pedro C. Magalhães & Maria Joana Soares, 2010. "Synchronism in Electoral Cycles: How United are the United States?," NIPE Working Papers 17/2010, NIPE - Universidade do Minho.
    15. Morales José F. & Song Tingting & Auerbach Arleen D. & Wittkowski Knut M., 2008. "Phenotyping Genetic Diseases Using an Extension of µ-Scores for Multivariate Data," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 7(1), pages 1-20, June.
    16. Hasanov, Mübariz & Araç, Aysen & Telatar, Funda, 2010. "Nonlinearity and structural stability in the Phillips curve: Evidence from Turkey," Economic Modelling, Elsevier, vol. 27(5), pages 1103-1115, September.
    17. Roger Girard & Norman Cliff, 1976. "A monte carlo evaluation of interactive multidimensional scaling," Psychometrika, Springer;The Psychometric Society, vol. 41(1), pages 43-64, March.
    18. Noah C Benson & Jeremy R Manning & David H Brainard, 2014. "Unsupervised Learning of Cone Spectral Classes from Natural Images," PLOS Computational Biology, Public Library of Science, vol. 10(6), pages 1-13, June.
    19. Kennen, Jonathan G. & Kauffman, Leon J. & Ayers, Mark A. & Wolock, David M. & Colarullo, Susan J., 2008. "Use of an integrated flow model to estimate ecologically relevant hydrologic characteristics at stream biomonitoring sites," Ecological Modelling, Elsevier, vol. 211(1), pages 57-76.
    20. W. Day & R. Sokal, 1989. "Classification Society of North America Twentieth Anniversary," Journal of Classification, Springer;The Classification Society, vol. 6(1), pages 169-170, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:89:y:2016:i:c:p:130-138. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.