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Nonlinear Dynamical Systems

[+] Author and Article Information
F. C. Moon

Department of Theoretical and Applied Mechanics, Cornell University, Ithaca NY 14853

Appl. Mech. Rev 38(10), 1284-1286 (Oct 01, 1985) (3 pages) doi:10.1115/1.3143693 History: Online June 12, 2009

Abstract

New discoveries have been made recently about the nature of complex motions in nonlinear dynamics. These new concepts are changing many of the ideas about dynamical systems in physics and in particular fluid and solid mechanics. One new phenomenon is the apparently random or chaotic output of deterministic systems with no random inputs. Another is the sensitivity of the long time dynamic history of many systems to initial starting conditions even when the motion is not chaotic. New mathematical ideas to describe this phenomenon are entering the field of nonlinear vibrations and include ideas from topology and analysis such as Poincaré maps, fractal dimensions, Cantor sets and strange attractors. These new ideas are already making their way into the engineering vibrations laboratory. Further research in this field is needed to extend these new ideas to multi-degree of freedom and continuum vibration problems. Also the loss of predictability in certain nonlinear problems should be studied for its impact on the field of numerical simulation in mechanics of nonlinear materials and structures.

Copyright © 1985 by American Society of Mechanical Engineers
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