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Four Applications of Nonlinear Analysis to Physics and Engineering

Marsden, Jerrold E. (1982) Four Applications of Nonlinear Analysis to Physics and Engineering. In: New directions in applied mathematics : papers presented April 25/26, 1980, on the occasion of the Case centennial celebration. Springer-Verlag , New York, pp. 85-107. ISBN 0387906045 http://resolver.caltech.edu/CaltechAUTHORS:20100825-090123755

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Abstract

My goal is to describe, in as accessible terms as possible, four separate applications of nonlinear analysis to relativity, elasticity, chaotic dynamics and control theory that I have recently been involved with. The descriptions are in some sense superficial since many interesting technical points are glossed over. However, this is necessary to efficiently convey the flavor of the methods. Most applications of mathematics to "real-life" problems of immediate need do not involve deep methods and ideas. For example, the force exerted on an aircraft frame by the landing gear when the vehicle lands is best computed, at least at first, by using undergraduate mathematics, engineering and experience. However, applied mathematics in the broad sense ranges from such problems of urgency to "practical" problems involving deeper mathematics (compute the lift and flutter characteristics for a design modification of the 747) through to fundamental physical problems involving interactions with the frontier of mathematics that need not be of any immediate "need" (is turbulence predictable from the Navier Stokes equations alone?). The applications I shall speak about are of the fundamental kind involving current research in mathematics and basic questions in physics and engineering that are normally not considered "practical". Most, if not all, of the other lectures I have heard at this conference fall into the same category


Item Type:Book Section
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http://www.cds.caltech.edu/~marsden/bib/1981/03-Ma1981/AuthorUNSPECIFIED
Additional Information:© 1980, Springer-Verlag. Research partially supported by NSF grant MCS 78-06718 and ARO grant DAAG 29-79C-0086.
Funders:
Funding AgencyGrant Number
NSFMCS 78-06718
Army Research Office (ARO)DAAG-29-79C-0086
Subject Keywords:Mathematics
Record Number:CaltechAUTHORS:20100825-090123755
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20100825-090123755
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19654
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:14 Sep 2010 17:27
Last Modified:26 Dec 2012 12:21

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