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Multiple Scales Theory
and Aerospace Applications
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Multiple Scales Theory
and Aerospace Applications
RudrapatnaV.Ramnath,Ph.D.
MassachusettsInstituteofTechnology
EDUCATIONSERIES
JosephA.Schetz
Editor-in-Chief
VirginiaPolytechnicInstituteandStateUniversity
Blacksburg,Virginia
Publishedby
AmericanInstituteofAeronauticsandAstronautics,Inc.
1801AlexanderBellDrive,Reston,VA20191-4344
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AmericanInstituteofAeronauticsandAstronautics,Inc.,Reston,Virginia
1 2 3 4 5
LibraryofCongressCataloging-in-PublicationData
Ramnath,RudrapatnaV.
Multiplescalestheoryandaerospaceapplications/RudrapatnaV.Ramnath.
p. cm.--(AIAAeducationseries)
Includesbibliographicalreferencesandindex.
ISBN978-1-60086-762-0
1. Aerospaceengineering--Dataprocessing.2. Aeronautics--Systemsengineering.3.
Differentiabledynamicalsystems.4. Scalinglaws(Statisticalphysics)I.Title.
TL563.R362010
629.10285--dc22
2010019966
Copyright©2010bytheAmericanInstituteofAeronauticsandAstronautics,Inc.Allrights
reserved.PrintedintheUnitedStatesofAmerica.Nopartofthispublicationmayberepro-
duced,distributed,ortransmitted,inanyformorbyanymeans,orstoredinadatabaseor
retrievalsystem,withoutthepriorwrittenpermissionofthepublisher.
Dataandinformationappearinginthisbookareforinformationalpurposesonly.AIAAis
notresponsibleforanyinjuryordamageresultingfromuseorreliance, nordoesAIAA
warrantthatuseorreliancewillbefreefromprivatelyownedrights.
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AIAAEducationSeries
Editor-In-Chief
JosephA.Schetz
VirginiaPolytechnicInstituteandStateUniversity
EditorialBoard
TakahiraAoki RakeshK.Kapania
UniversityofTokyo VirginiaPolytechnicInstitute
andStateUniversity
JoãoLuizF.Azevedo
InstitutodeAeronáuticaeEspaço BrianLandrum
SãoJosédosCampos, UniversityofAlabama
Brazil inHuntsville
KarenD.Barker TimothyC.Lieuwen
GeorgiaInstitute
ofTechnology
RobertH.Bishop
UniversityofTexasatAustin
MichaelMohaghegh
TheBoeingCompany
AaronR.Byerley
U.S.AirForceAcademy
ConradF.Newberry
RichardColgren
BrettNewman
UniversityofKansas
OldDominionUniversity
JamesR.DeBonis
JosephN.Pelton
NASAGlennResearchCenter
GeorgeWashingtonUniversity
KajalK.Gupta MarkA.Price
NASADrydenFlightResearchCenter Queen’sUniversityBelfast
RikardB.Heslehurst DavidM.VanWie
UniversityofNewSouthWales JohnsHopkinsUniversity
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Dedicated to
the fond memory of my parents,
Sri R.Venkataramaiya and Smt. Seethamma
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Foreword
MultipleScalesTheoryandAerospaceApplicationsconstitutesacomprehen-
siveworkonthepowerfultechniqueofmultiplescalesthatcombinestheoretical
conceptsandpracticalapplicabilityinasynergistictreatment.Thetableofcontents
ofthisbooklistsasetoftopicsthatwouldbefamiliartothewell-informedapplied
mathematicianworkinginthefieldofaerospaceengineering.Thisdoesnotmean
thatthebookisdirectedonlyattheappliedmathematician;indeed,theoppositeis
moreasymptoticallycorrect.Thisbookcanandshouldbestudiedforhandsome
returns by the applied dynamics and control analysts and designers, simulation
specialists,andthoseexperimentalistsworkinginaerospaceengineering.
RudrapatnaV.Ramnath,aproductofthePrincetonUniversityHayes–Kruskal
Schoolformodelingandanalysisofnon-linearproblems,haspresentedhereina
highlevelofintellectualrigor,derivedfromhiswideexperienceinbothacademia
andtheaerospaceindustry.Hehasbeenintimatelyinvolvedinthedetailedproblem
formulationandsolutionoftheapplicationspresentedinthebook.Ihastentopoint
out the depth and breadth of Professor Ramnath’s experiences as a practicing
aerospace engineer allow for a theoretical approach that is well balanced with
usefulappliedandphysics-basedresults.Hewritesfromapracticalperspective.
PerhapsthestrongestthemethatformsthefoundationofthebookisProfessor
Ramnath’sbeliefthatcomplex,ambiguousproblemsinaerospaceengineeringare
notareasonforsloppyorcarelessproblemsolving.Tothecontrary, hedelivers
usefulresultsinthesesituationsbasedongreatcare,rigor,andingenuityinapply-
ingquantitativemultiplescalesapproximationsthatarebasedonhisgeneralization
ofthetechniqueanddistillinghisexperienceonmanyaerospaceapplications.
Not only do I agree with Professor Ramnath on the demand and utility of
rigor and care for correctness, I believe it to be essential for progress, safety,
andsustainabilityinaerospaceengineering.Therefore, Ihighlyrecommendthis
booktopracticingdynamicsandcontrolanalysts,designers,simulationspecialists,
experimentalists,andappliedmathematiciansinaerospaceengineeringatalllevels
whodesiretobecomebetterandmorecreativeintheirprofession.
WesleyL.Harris
PhD.NAE,AIAAFellow
MassachusettsInstituteofTechnology
Cambridge,Massachusetts
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