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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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