Eulerian and Lagrangian Descriptions

Sohrob Mottaghi; Rene Gabbai; Haym Benaroya

doi:10.1007/978-3-030-26133-7_6

Eulerian and Lagrangian Descriptions

Sohrob Mottaghi, Rene Gabbai, Haym Benaroya

School of Engineering, Mechanical & Aerospace Engineering

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

This chapter derives the relations between Eulerian and Lagrangian descriptions of displacement and velocity fields, relations between the time derivatives of system properties, variations, and introduces Jourdainâ€™s variational principle. Jourdainâ€™s principleÂ is then applied to viscous incompressible fluids, and the derivation of the energy rate equation. These equations will be utilized in the subsequent chapter for the derivation of the flow-oscillatorÂ model for vortex-induced vibration.

Original language	English (US)
Title of host publication	Solid Mechanics and its Applications
Publisher	Springer Verlag
Pages	143-187
Number of pages	45
DOIs	https://doi.org/10.1007/978-3-030-26133-7_6
Publication status	Published - Jan 1 2020

Publication series

Name	Solid Mechanics and its Applications
Volume	260
ISSN (Print)	0925-0042
ISSN (Electronic)	2214-7764

Fingerprint

All Science Journal Classification (ASJC) codes

Civil and Structural Engineering
Automotive Engineering
Aerospace Engineering
Acoustics and Ultrasonics
Mechanical Engineering

Cite this

Mottaghi, S., Gabbai, R., & Benaroya, H. (2020). Eulerian and Lagrangian Descriptions. In Solid Mechanics and its Applications (pp. 143-187). (Solid Mechanics and its Applications; Vol. 260). Springer Verlag. https://doi.org/10.1007/978-3-030-26133-7_6

@inbook{e4bb4960b3fc4da794c1cccc9c9cb9c9,

title = "Eulerian and Lagrangian Descriptions",

abstract = "This chapter derives the relations between Eulerian and Lagrangian descriptions of displacement and velocity fields, relations between the time derivatives of system properties, variations, and introduces Jourdain{\^a}€™s variational principle. Jourdain{\^a}€™s principle{\^A} is then applied to viscous incompressible fluids, and the derivation of the energy rate equation. These equations will be utilized in the subsequent chapter for the derivation of the flow-oscillator{\^A} model for vortex-induced vibration.",

author = "Sohrob Mottaghi and Rene Gabbai and Haym Benaroya",

year = "2020",

month = "1",

day = "1",

doi = "10.1007/978-3-030-26133-7_6",

language = "English (US)",

series = "Solid Mechanics and its Applications",

publisher = "Springer Verlag",

pages = "143--187",

booktitle = "Solid Mechanics and its Applications",

address = "Germany",

}

TY - CHAP

T1 - Eulerian and Lagrangian Descriptions

AU - Mottaghi, Sohrob

AU - Gabbai, Rene

AU - Benaroya, Haym

PY - 2020/1/1

Y1 - 2020/1/1

N2 - This chapter derives the relations between Eulerian and Lagrangian descriptions of displacement and velocity fields, relations between the time derivatives of system properties, variations, and introduces Jourdainâ€™s variational principle. Jourdainâ€™s principleÂ is then applied to viscous incompressible fluids, and the derivation of the energy rate equation. These equations will be utilized in the subsequent chapter for the derivation of the flow-oscillatorÂ model for vortex-induced vibration.

AB - This chapter derives the relations between Eulerian and Lagrangian descriptions of displacement and velocity fields, relations between the time derivatives of system properties, variations, and introduces Jourdainâ€™s variational principle. Jourdainâ€™s principleÂ is then applied to viscous incompressible fluids, and the derivation of the energy rate equation. These equations will be utilized in the subsequent chapter for the derivation of the flow-oscillatorÂ model for vortex-induced vibration.

UR - http://www.scopus.com/inward/record.url?scp=85071506657&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85071506657&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-26133-7_6

DO - 10.1007/978-3-030-26133-7_6

M3 - Chapter

AN - SCOPUS:85071506657

T3 - Solid Mechanics and its Applications

SP - 143

EP - 187

BT - Solid Mechanics and its Applications

PB - Springer Verlag

ER -

Access to Document

10.1007/978-3-030-26133-7_6