Rigid body dynamics for space applications

422 Pages·2017·19.692 MB·English

by  Aslanov, Vladimir S.

RIGID BODY
DYNAMICS
FOR SPACE
APPLICATIONS
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RIGID BODY
DYNAMICS
FOR SPACE
APPLICATIONS
VLADIMIR S. ASLANOV
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DEDICATION
To my parents, and wife Lyudmila
–Vladimir S. Aslanov
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CONTENTS
Preface ix
1. Mathematical Mechanical Preliminaries 1
1.1 Mathematics 1
1.2 RigidBodyKinematic 6
1.3 RigidBodyDynamics 13
1.4 ChaoticMotion 17
References 23
2. Reentry Attitude Dynamics 25
2.1 Introduction 25
2.2 AerodynamicsofReentryVehicles 26
2.3 TheEquationsofMotion 33
2.4 AnalyticalSolutionsoftheUndisturbedEquationforSinusoidal
AerodynamicMoment 44
2.5 AnalyticalSolutionsoftheUndisturbedEquationforBiharmonical
AerodynamicMoment 49
2.6 QuasistaticSolutionsfortheDisturbedEquationofMotion 59
2.7 AdiabaticInvariantsandtheApproximateSolutionfor
theDisturbedMotion 60
2.8 BifurcationandWaysofItsEliminationattheDescentofSpacecraftin
theRarefiedAtmosphere 68
2.9 ChaoticAttitudeMotionofReentryVehicleWithanInternal
MovingMass 85
2.10 ChaoticBehaviorofBodiesinaResistantMedium 94
2.11 ChaoticMotionofaReentryCapsuleDuringDescentintothe
Atmosphere 109
References 121
3. Dynamics andControl ofCoaxial Satellite Gyrostats 127
3.1 Introduction 127
3.2 AttitudeMotionEquations 129
3.3 IntegrableCasesintheDynamicsofCoaxialGyrostats 135
3.4 TheExactAnalyticalSolutions 141
3.5 DynamicsandChaosControloftheGyrostats 153
vii
viii Contents
3.6 DynamicsandControlofDual-SpinGyrostatSpacecraftWith
ChangingStructure 159
3.7 AdiabaticInvariantsintheDynamicsofAxialGyrostats 166
References 175
4. Deployment, Dynamics, and Controlof a Tether-Assisted
Return Mission of a Reentry Capsule 179
4.1 Introduction 179
4.2 MathematicalModelofaSatelliteWithaTetheredPayload 182
4.3 AnalyticalSolutionintheCaseofaSlowChangingoftheParameters 192
4.4 OscillationsoftheSatelliteWithaVerticalElasticTether 202
4.5 OscillationsintheCaseofanEllipticOrbit 220
4.6 SwingPrincipleforDeploymentofaTether-AssistedReturnMission
ofaReentryCapsule 230
4.7 Tether-AssistedReturnMissionFromanEllipticalOrbitTakingInto
AccountAtmosphericStageofReentry 240
References 250
5. Removalof LargeSpaceDebris by a Tether Tow 255
5.1 Introduction 255
5.2 DynamicsofOrbitalDebrisConnectedtoSpacecraftbyaTetherina
FreeSpace 256
5.3 DynamicsofLargeOrbitalDebrisRemovalUsingTetheredSpace
TugintheEarth’sGravitationalField 271
5.4 BehaviorofTetheredDebrisWithFlexibleAppendages 286
5.5 Dynamics,AnalyticalSolutionsandChoiceofParametersforTowed
SpaceDebrisWithFlexibleAppendages 295
5.6 TheMotionofTetheredTug-DebrisSystemWithFuelResiduals 308
5.7 DynamicsofTowedLargeSpaceDebrisTakingIntoAccountAtmospheric
Disturbance 323
5.8 ChaosBehaviorofSpaceDebrisDuringTetheredTow 342
References 353
6. Original Tasks of Space Mechanics 357
6.1 Introduction 357
6.2 GravitationalStabilizationoftheSatelliteWithaMovingMass 358
6.3 TheDynamicsoftheSpacecraftofVariableComposition 371
6.4 RestorationofAttitudeMotionofSatelliteUsingSmallNumbersof
TelemetryMeasurements 383
References 399
Index 401
PREFACE
SovietsputnikusheredinthespaceerainOct.1957.Thislaunchoccurred
almost70yearsagoandnonethelessinterestinthecreationanduseofspace
technicscontinuesunabated.Newchallengesformulatenewideas,whichbe
implemented in the new space programs. Currently, global unexpected,
including, and environmental concerns associated with big population of
nonfunctional and abandoned satellites, spent upper stages and fragments.
Each new space program is unique and requires new technologies and
carefulresearchbasedonmathematicalmodeling.Resultsofthemathemat-
ical simulation and the analytical solutions allow a better understanding of
the phenomenon and processes of spacecraft functioning, and choose the
conceptual design of future aerospace systems. Most of the space systems
can be considered as a system of rigid bodies, and in some cases, with
additional elastic and viscoelastic elements, and with fuel residuals.
Thepurposeofthebookistoshowthenatureofthephenomenaandto
explainfeaturesofthebehaviorofspaceobjects,asasystemofrigidbodies,
basedontheknowledgeofclassicalmechanics,regularandchaoticdynam-
ics. The author tried to show relatively simple ways of constructing
mathematicalmodelsandanalyticalsolutionsdescribingthebehaviorofvery
complex mechanical systems. The book contains many analytical and
approximate analytical solutions that help to understand the nature of the
studied phenomena. It is based on the recent papers of the author in
international journals, which have been reviewed by leading scientists of
the world, thus the results can be trusted. This book covers modern prob-
lemsofspaceflightmechanics,suchasattitudedynamicsofreentrycapsulein
Earth’s atmosphere, dynamics and control of coaxial satellite gyrostats,
dynamics and control of a tether-assisted return mission, removal of large
space debris by a tether tow.
Theauthorhopesthatthisbookwillbehelpfulfor awiderangeofsci-
entists,engineers,graduatestudents,universityteachers,andstudentsinthe
fieldsofmechanics,andaerospacescience.Graduatestudentsandresearchers
find in the book the new results of studies in a wide range of aerospace
applications, and they can also use it as tool for obtaining new knowledge.
Aerospaceengineerscangetengineeringapproachestothedevelopmentof
new space systems. University teachers can use the text for preparation of
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