Table Of ContentToPapa,Prachi,andManya
Ashish Tewari
Atmospheric and Space
Flight Dynamics
Modeling and Simulation with
MATLAB(cid:2)R and Simulink(cid:2)R
Birkha¨user
Boston • Basel • Berlin
AshishTewari
DepartmentofAerospaceEngineering
IndianInstituteofTechnology,Kanpur
IIT-Kanpur208016
India
MathematicsSubjectClassification:00A71,00A72,65L06,70B05,70B10,70E05,70E15,70E20,
70E50,70F05,70F07,70F10,70F15,70G60,70H03,70J10,70J25,70J35,70K05,70M20,70P05,
70Q05,74F10,76G25,76H05,76J20,76K05,76L05,76N15,76N20,93A30,93B52,93B55,93B60,
93C05
LibraryofCongressControlNumber:2006935811
ISBN-10:0-8176-4437-7 e-ISBN-10:0-8176-4438-5
ISBN-13:978-0-8176-4437-6 e-ISBN-13:978-0-8176-4438-3
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Preface
Itisfittinginthisbeginningofthesecondcenturyofpoweredflighttobewrit-
ing a book on flight dynamics—in particular,the modeling and simulation of
flightdynamics.Noonehadheardofflightdynamics,orindeed,modelingand
simulation,intheearlydaysofaviation.PioneerssuchastheWrightbrothers,
Langley,Curtiss,andBleriotpreferredexperimentationwithflyingmodels to
working with the equations of motion. Until the 1940s, flight dynamics was
more of an art than an engineering discipline, with books such as Stick and
Rudder: An Explanation of the Art of Flying byLangewiesche(McGraw-Hill,
1944) imparting a fundamental, but purely qualitative understanding of air-
plane flight, which was useful to both budding aeronautical engineers and
pilots.AftertheSecondWorldWar,largestridesmadeinmathematicalmod-
eling of airplane flight dynamics were first documented in classicaltexts such
as Airplane Performance, Stability and Control by Perkins and Hage (Wiley,
1949), which covered linearized, time-invariant flight dynamics, and inspired
a multitude of textbooks in the field, such as those by Etkin, McCormick,
Miele, etc. With the advent of supersonic, hypersonic, and space flight in
the 1950s and 1960s, there was a great need for modeling and simulation of
high-performanceflight dynamics, which essentiallyinvolves a set of coupled,
time-varying,nonlinear,ordinarydifferentialequations.While a sprinkling of
mathematical models for high-speed flight was available in the introductory
texts of the 1960s and 1970s,a thorough analytical treatment of these topics
was confined to specialized technical reports. Yet, there was little mention of
numericalmodelingandsimulation.Researcharticlesfirstbegantoappearin
the 1960s, which presented numerical calculations for special examples with
analog—andlater—digitalcomputers,concerninghigh-performanceflightdy-
namics. As numericalscience evolvedand computing power grew,the sophis-
tication of flight dynamic modeling and simulation progressed to missiles,
launch vehicles, re-entry vehicles, and spacecraft. Guidance and navigation
for the manned lunar missions (1968–72) essentially utilized such numerical
capability. Numerical modeling and simulation of flight dynamics has now
emerged as a major discipline.
vi Preface
Thechiefmotivationforwritingthisbookistopresentaunifiedapproach
to both aircraft and spacecraft flight dynamics. Modern aerospace vehicles,
such as the space shuttle, other launch vehicles, and long-range ballistic mis-
siles,donotdiscriminatebetweenatmosphericandspaceflight.Unfortunately,
nearly all textbooks on flight dynamics do so, and seldom do we find aircraft
and spacecraft co-existing within the covers of the same book. Many excel-
lent textbooks are available on modern aircraft dynamics (such as those by
Zipfel, Pamadi, Stengel, Etkin, and Schmidt), but they stop short of hyper-
sonic aircraft and sub-orbital trajectories. Similarly, the available textbooks
on space dynamics (Hale, Brown, Curtis, etc.) do not go below hypersonic
speeds ofre-entryvehicles.While it is easy to understand the separateevolu-
tionofaircraftandspacecraftinthepast,thefutureofflightliesinintegrating
the two vehicles into a single unit. The single-stage-to-orbit(SSTO) reusable
launchvehicle, which takesoff and lands like anaircraftand deliverspayload
to an orbiting space station, exemplifies the vision of aerospace engineering
for the future. Therefore, it is imperative that this new generation of engi-
neers is taught to remove the artificial distinction between atmospheric and
space flight. Many aerospace engineering departments realize this need, of-
fering courses that integrate atmospheric and space flight. Examples of such
courses are AE-520 Flight Vehicle Dynamics, AE-580 Analytical Methods in
Aeronautical and Astronautical Engineering, and AE-621 Aircraft and Space-
craft Automatic Control Systems, offered by the Department of Aerospace
Engineering at Ohio State University.
Thisbookisanattempttobridgethe gapbetweenaircraftandspacecraft
dynamics,bydemonstratingthatthetwoevolvelogicallyfromthesamesetof
physicalprinciples.Thebreadthoftopicscoveredisunparalleledbyanyother
book on the subject. Beginning with kinematics and translational dynamics
overarotatingplanet,nonsphericalgravitymodel,leadingtotwo-bodyorbits,
orbital maneuvers, rendezvous in space, and lunar and interplanetary travel,
atmospheric flight follows logically after chapters on atmospheric modeling,
aerodynamics, and propulsion. The attitude dynamics and control of aircraft
and spacecraft are presented in an integrated and continuous fashion. Mod-
eling of nonlinear flight dynamics is covered in numerous examples, such as
simulation of long-range airplane flight, supermaneuvers, rocket ascent, sub-
orbitalflightandatmosphericentry,multi-axisrotationsofspacecraft,andin-
ertiacoupled,open-andclosed-loopairplanedynamics,whicharenotfoundin
othertextbooksonflightdynamics.The bookculminateswithafinalchapter
covering advanced concepts with six-degree-of-freedom simulation examples,
and modeling of structural dynamics, unsteady aerodynamics, aeroelasticity,
and propellant slosh dynamics. From the solved examples, the reader can
easily build his/her own simulations as independent semester projects. The
choice of gravitational models, coordinate frames, attitude control systems,
propulsion systems, and flow models to use is left up to the reader, in order
to provide an almost unlimited capability to build various simulations.
Preface vii
This book is primarily designed as a textbook for junior and senior un-
dergraduates,aswellasgraduatestudents inmechanical,aerospaceengineer-
ing/aeronautics, and astronautics departments. The book may also be used
as a reference for practicing engineers and researchers in aerospace engineer-
ing, aeronautics, and astronautics, whose primary interest lies in modeling
and simulation of flight dynamics. The contents have evolved from the lec-
ture notes of several 3rd–4th year undergraduate, and graduate-level courses
I havetaughtoverthepast14years.Thematerialinthebook hasbeenespe-
cially selected to be useful in a modern course on flight dynamics, where the
artificial distinction between atmospheric and space flight is removed. At the
same time, the material offers the choice of being adopted in separate tradi-
tional courses on space dynamics and atmospheric flight mechanics. In this
respect,the textis quiteflexibleandcanbe utilizedbyeventhoseinstructors
whodonotnecessarilyagreewiththecomprehensiveapproachadoptedinthe
book.Itis,however,suggestedthatthemixofatmosphericandspacedynam-
ics be retained in each course. A detailed discussion of the usage of material
by course instructors is given below. The chapters are designed to follow in
a sequence such that their concepts evolve logically and fit into each other
like a glove. The concepts are introduced in an easy-to-read manner, while
retaining mathematical rigor. The theory behind flight dynamic modeling is
highlighted and fundamental results are derived analytically. Examples and
problems have been carefully chosen to emphasize the understanding of un-
derlying physicalprinciples. Eachchapterbegins with a list ofclearlydefined
aimsandobjectives.Atthe endofeachchapter,shortsummariesandanum-
berofexercisesareprovidedinordertohelpreadersconsolidatetheirgraspof
thematerialpresented.Answerstoselectedproblemsareincludedattheback
ofthebooksothatareadercanverifyhis/herownsolutions.Fullstep-by-step
solutionstoallofthe exerciseswillbe availableuponrequestto the publisher
in a separate solutions manual designed for course instructors to use with
their students. The manual may also be made available to researchers and
professionals (nonstudents) who are using the book for self-study purposes.
Requests for the solutions manual should be sent to the publisher on an of-
ficial letterhead with full particulars, including the course name and number
for which the book is being adopted.
Perhaps the greatest distinguishing feature of the book is the ready and
(cid:2) (cid:2)
extensive use of MATLAB and Simulink ,1 as practical computational
tools to solve problems across the spectrum of modern flight dynamics. The
MATLAB/Simulinkcodesareintegratedwithinthetextinordertoreadilyil-
lustratemodelingandsimulationofaerospacedynamics.MATLAB/Simulink
is standard, easy-to-use software that most engineering students learn in the
firstyearoftheircurriculum.Withoutsuchasoftwarepackage,thenumerical
examples and problems in a text of this kind are difficult to understand and
(cid:2)
1 MATLAB/Simulink are registered products of The MathWorks, Inc., 3 Apple
Hill Drive, Natick,MA 01760-2098, U.S.A.http://www.mathworks.com.
viii Preface
solve. In giving the reader a hands-on experience with MATLAB/Simulink
as applied to practical problems, the book is useful for a practicing engi-
neer, apart from being an introductory text for the beginner. The book uses
the software only as an instructional tool, discouraging the “black-box” ap-
proachfound in many textbooks that carry “canned” software.The reader is
required to write his/her own codes for solving many of the problems con-
tained as exercises. An appendix contains a brief review of some important
methods of numerically integrating ordinary differential equations that are
commonly encountered in flight dynamics. In summary, the primary features
of this book are a unified approach to aircraft and spacecraft flight, a wide
range of topics, nontrivial simulations, logical and seamless presentation of
material, rigorous analytical treatment that is also easy to follow, and a
ready use of MATLAB/Simulink software as an instructional tool. All the
codesusedinthe bookareavailablefordownloadingatthe followingwebsite:
http://home.iitk.ac.in/∼ashtew/page10.html.
Thetextfocusesonthemodelingandsimulationaspectsofflightmechan-
ics in a wide range of aerospace applications. This treatment is more general
than that found in many textbooks on atmospheric flight dynamics, which
only cover the approximate equations of motion offering analytical closed-
formsolutions(consideredtrivialfromamodelingandsimulationviewpoint).
However, it is recognized that the analytical solutions impart an insight into
the science of flight dynamics, especially in a junior-level course. For this
reason, the discussion of approximate, analytical solutions to special flight
situations is offered in the form of exercises at the end of the chapters. The
reader is referred to traditional flight mechanics texts for details on approx-
imate, analytical treatment wherever necessary. A course instructor has the
freedomto begin with the generalderivations of the equations of motionpre-
sented in the book, proceeding to the special approximate flight situations
(planar, quasi-steady, constant mass, flat nonrotating earth, etc.) for which
the traditional, analytical solution is available.
A reader is assumed to have taken basic undergraduatecourses in mathe-
maticsandphysics—particularlycalculus,linearalgebra,anddynamics—and
is encouraged to review these fundamental concepts at several places in the
text. I will now briefly discuss the organization and highlights of the topics
covered in each chapter in order to provide a ready guide to the reader and
the classroom instructor. This will help readers and instructors select what
parts of the book will be relevant either in a particular course, or for specific
professional study and reference.
It is sometimes felt that a “logical” sequence of topics should begin with
atmospheric flight and end with space flight. While such an “earth-to-space”
arrangementmayappearnaturalinadocumentaryonflight,itisnotsuitable
for a textbook. As pointed out above, the material in the text has been or-
dered such that the physical and mathematical concepts evolve logically and
sequentially. Chapters 2–4, which cover kinematics and analytical dynamics,
areequallyrelevanttobothspaceandatmosphericflight.Thenextthreechap-
Preface ix
ters (5–7) on orbital mechanics logically follow from this foundation, as they
do not require a model of the atmosphere and aerodynamics. Chapter 8, on
rocketpropulsion,followsfor thesame reason.However,before beginning the
treatment on atmospheric flight, it is necessary to introduce an atmospheric
model, aerodynamic concepts, and air-breathing propulsion, which are car-
ried out in Chapters 9–11. I would add that for an undergraduate student
in flight dynamics, the introductory chapters on aerodynamics and propul-
sion (Chapters 8–11) are especially relevant. Chapters 12–14—the “meat” of
the book—put together the concepts of the foregoing chapters in order to
present a comprehensive modeling, simulation, control, and analysis of at-
mospheric, trans-atmospheric, and space trajectories. Chapter 15 culminates
the treatment with advancedmodeling and simulationconcepts applicable to
aerospace vehicles. Hence, the first four and the last four chapters pertain to
both atmospheric and space flight, whereas the intervening chapters present
specialized treatment of either of the two aspects of flight. The following is a
detailed overviewof each chapter:
Chapter 1 offers a basic introduction and motivation for studying flight
dynamics in a comprehensive manner and includes the classification of flight
vehicles, as well as the important assumptions made in their modeling and
simulation.
Chapter 2 presents the kinematic modeling and coordinate transforma-
tions useful in all aspects of flight dynamic derivations. The rigorous vector
analysisof rotationalkinematics is presentedwith many numericalexamples.
Basicidentities—suchasthetime derivativeofavector,itsrotation,andrep-
resentation in various reference frames—are derived in a manner that can be
easily utilized for derivation of both translationaland rotationalequations of
motion in subsequent chapters. Several alternative kinematic representations
[Eulerangles,Euler-axis/principalrotation,rotationmatrix,Eulersymmetric
parameters (quaternion), Rodrigues and modified Rodrigues parameters] are
introduced and their time-evolution derived. A reader can cover the first two
sections in a first reading, proceed to Chapters 3–12, and then return to the
other sections of Chapter 2 before beginning Chapter 13.
Chapter 3 discusses planetary shape and gravity. While a spherical grav-
ity model serves most atmospheric flight applications reasonably well, it is
necessary to model the spherical harmonics of a nonspherical mass distribu-
tion(Sections3.2–3.4)foraccuratespace-flight,rocket-ascent,andentry-flight
trajectories.
Chapter 4 is an introduction to analytical dynamics. While presenting
the analyticaltools for deriving a generalmodel for translationalmotion, the
chapter also discusses the relationship between translational and rotational
dynamics of a flight vehicle. This chapter is essentially the starting point for
derivingthebasickineticequationsforaerospaceflight,andincludesdynamics
in movingframes,variablemass bodies, the N-bodygravitationalproblemin
spacedynamics,anditsspecializationtotwo-bodytrajectorieswithanalytical
and numerical solutions. The problems at the end of the chapter test the
