Nichtlineare Mechanik Book by H. Kauderer - Bookswagon
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Nichtlineare Mechanik

Nichtlineare Mechanik


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About the Book

Fast alle Probleme der Mechanik, die man mathematisch durch eine lineare Differentialgleichung zu formulieren pflegt, sind, streng- genommen, nichtlinear, d. h. sie miiBten eigentlich durch eine nicht- lineare Differentialgleichung ausgedriickt werden. Man hat die Probleme lediglich deshalb linearisiert, um den mathematischen Schwierigkeiten, die solche Differentialgleichungen bereiten, aus dem Wege zu gehen und dafiir die gut ausgebildete und iibersichtliche Theorie der linearen Differentialgleichungen anwenden zu konnen. Auf zwei wichtige Zweige der Mechanik hat man dieses Verfahren der Linearisierung besonders konsequent angewandt, niimlich auf die Elastostatik und auf die Schwingungslehre. So wurden zwei Lehr- gebiiude der linearisierten Theorie errichtet, deren Gestalt im groBen und in vielen Einzelheiten heute schon endgiiltig geformt ist. All- miihlich sind nun aber auch die Unzuliinglichkeiten zutage getreten, die diesen klassischen linearisierten Theorien anhaften. Sie bestehen einerseits darin, daB sie die tatsiichlichen mechanischen Vorgiinge nur geniihert beschreiben und daher hohere Anspriiche an Genauigkeit oft nicht erfiillen konnen, und andererseits, was noch viel schwerer wiegt, in der Tatsache, daB das Linearisierungsverfahren die Struktur ge- wisser Differentialgleichungen so stark andert, daB zahlreiche inter- essante Erscheinungen auch rein qualitativ iiberhaupt nicht mehr wiedergegeben und somit aus dem Komplex der tatsachlich auftreten- den physikalischen Vorgiinge von vornherein ausgesiebt werden. Durch die Anwendung, welche die Mechanik in der Technik in den letzten Jahrzehnten erfahren hat, erwies sich aber nun gerade eine Steigerung der Genauigkeit und eine Beschreibung der durch die lineare Theorie nicht erfaBbaren Effekte, die in der Technik teilweise jetzt schon eine wichtige Rolle spielen, als dringend erwiinscht.


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Product Details
  • ISBN-13: 9783642927348
  • Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
  • Binding: Paperback
  • Height: 234 mm
  • No of Pages: 684
  • Series Title: German
  • Weight: 1015 gr
  • ISBN-10: 3642927343
  • Publisher Date: 21 Jan 2012
  • Edition: Softcover Reprint of the Origi ed.
  • Language: German
  • Returnable: N
  • Spine Width: 36 mm
  • Width: 156 mm


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