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Fractional Dynamics: A Statistical Perspective

[+] Author Affiliations
J. A. Tenreiro Machado, Alexandra Galhano

Institute of Engineering of Porto, Porto, Portugal

Paper No. DETC2007-34340, pp. 233-237; 5 pages
doi:10.1115/DETC2007-34340
From:
  • ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 5: 6th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C
  • Las Vegas, Nevada, USA, September 4–7, 2007
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 0-7918-4806-X | eISBN: 0-7918-3806-4
  • Copyright © 2007 by ASME

abstract

Fractional calculus is a mathematical paradigm that has been increasingly adopted to describe the dynamics of systems with hereditary characteristics, or that reflect an average of a large population of micro elements. In this line of thought, this article analyzed the statistical dynamics of a system composed of a large number of micro-mechanical masses with backlash and impacts. We conclude that, while individual dynamics of each element has an integer order nature, the global dynamics reveal the existence of both integer and fractional dynamics.

Copyright © 2007 by ASME

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