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Euler’s Equations

S. G. Rajeev

in Fluid Mechanics: A Geometrical Point of View

Published in print:
2018
Published Online:
October 2018
ISBN:
9780198805021
eISBN:
9780191843136
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198805021.003.0002
Subject:
Physics, Soft Matter / Biological Physics, Condensed Matter Physics / Materials

Euler derived the fundamental equations of an ideal fluid, that is, in the absence of friction (viscosity). They describe the conservation of momentum. We can derive from it the equation for the ... More


The Consequences of Extensivity

Robert H. Swendsen

in An Introduction to Statistical Mechanics and Thermodynamics

Published in print:
2012
Published Online:
December 2013
ISBN:
9780199646944
eISBN:
9780191775123
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199646944.003.0013
Subject:
Physics, Condensed Matter Physics / Materials

Although extensivity is not an essential property of thermodynamic systems, it is a very useful concept for analysing the properties of materials when we can ignore surface and boundary effects. This ... More


Bernoulli’s equation

Marcel Escudier

in Introduction to Engineering Fluid Mechanics

Published in print:
2017
Published Online:
January 2018
ISBN:
9780198719878
eISBN:
9780191840180
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198719878.003.0007
Subject:
Physics, Soft Matter / Biological Physics, Condensed Matter Physics / Materials

In this chapter Newton’s second law of motion is used to derive Euler’s equation for the flow of an inviscid fluid along a streamline. For a fluid of constant density ρ‎ Euler’s equation can be ... More


The rigid body

S. G. Rajeev

in Advanced Mechanics: From Euler's Determinism to Arnold's Chaos

Published in print:
2013
Published Online:
December 2013
ISBN:
9780199670857
eISBN:
9780191775154
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199670857.003.0005
Subject:
Physics, Atomic, Laser, and Optical Physics

In this chapter, the moment of inertia is defined and Euler's equations for the rigid body are derived. They can be solved in terms of Jacobi elliptic functions.


Fluid Mechanics: A Geometrical Point of View

S. G. Rajeev

Published in print:
2018
Published Online:
October 2018
ISBN:
9780198805021
eISBN:
9780191843136
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198805021.001.0001
Subject:
Physics, Soft Matter / Biological Physics, Condensed Matter Physics / Materials

Starting with a review of vector fields and their integral curves, the book presents the basic equations of the subject: Euler and Navier–Stokes. Some solutions are studied next: ideal flows using ... More


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