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2018 | OriginalPaper | Chapter

25. One-Dimensional Continuous Systems

Authors : Antonio Romano, Addolorata Marasco

Published in: Classical Mechanics with Mathematica®

Publisher: Springer International Publishing

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Abstract

In this chapter, a brief introduction to one-dimensional continuous systems is presented. First, the balance equations relative to these systems are formulated: the mass conservation and the balance of momentum and angular momentum. Then, these equations are applied to describe the behavior of Euler’s beam. Further, the simplified model of wires is introduced to describe the suspension bridge and catenary. Finally, the equation of vibrating strings is derived and the corresponding Sturm–Liouville problem is analyzed. In particular, the homogeneous string is studied by D’Alembert solution.

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previous chapter An Introduction to Celestial Mechanics
next chapter An Introduction to Special Relativity
Footnotes
1
This principle postulates that if forces act only on the bases of S, then the deformation of S depends only on the total force and torque acting on the bases of S, not on their distribution, except for the regions very close to the bases.
 
2
For the sake of simplicity we omit the dependence of \(\overline{s}\) on \(s_*\) and t.
 
3
The reader is invited to analyze the case \(\lambda <0\).
 
Metadata
Title
One-Dimensional Continuous Systems
Authors
Antonio Romano
Addolorata Marasco
Copyright Year
2018
Book
Classical Mechanics with Mathematica®

Print ISBN: 978-3-319-77594-4

Electronic ISBN: 978-3-319-77595-1

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-77595-1_25

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