Thesis - Leigh Moody.pdf - Bad Request - Cranfield University

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Chapter 6 / Missile Guidance _ _ ∂ F ∂ P XB T ZG d, m : = ⎛ 6 6. 7881 x 10 ⎞ ∂ P − ⎜ ⎟ ⎜ ⋅ 0. 833 XB PS F ⎟ ⎝ ⋅ T ⎠ ∂ P 6-6 S ZG d, m Equation 6.3-4 Short-boosting missiles remain in the Troposphere in which case the variation in static pressure is given by Equation 19.1-4. 6.4 Missile Drag The boost and coast phase drag depends on Mach number (Mm) and air density (ρA) defined in §19.3, also missile speed and body incidence ( MV ξ B ) defined in §16.6, D XB D −1 2 2 ⋅ π ⋅ ρA ⋅ dm ⋅ P& d, m F : = − 8 ⋅ C ij i MV MV ( M ) ⋅ N ( 24 ⋅ ξ ) C : = CD ⋅ M ξ m j B D MAX Equation 6.4-1 B Equation 6.4-2 The drag coefficient (CD) is determined using the B-splines coefficients (CDij) listed in Table 6-1 for Mach numbers [1,4], and body incidence [0,24°]. The boost phase variation in (CD) for Mach numbers and incidence up to 3.5 and 15° respectively is shown in Figure 15-1. BOOST PHASE COEFFICIENT 1.4 1.2 1 0.8 0.6 0.4 0.2 1 1.5 2 2.5 3 3.5 MISSILE MACH NUMBER SIGMA = 0 deg SIGMA = 5 deg SIGMA = 10 deg SIGMA = 15 deg Figure 6-2 : Boost Phase Drag Coefficient The equivalent coast phase drag (not shown) is larger as the effective missile surface area increases without the motor plume. To accommodate variations in maximum incidence (σMAX), defaulting to 40°, the output from the B-splines are scaled by 40/24. The drag function state dependencies are,
Chapter 6 / Missile Guidance _ _ − ϕ CSA ⋅ ρ A ZG 2 ZG ZG MV ZG B B G ( P ) ⋅ P& ⋅ C ( M ( P , P& ) , ξ ( P , T ( Q ) ⋅ P& ) ) d, m d, m D m 6-7 F XB D d, m : = d, m The drag force variation with geodetic height, ∂ F ∂ P XB D ZG d, m : = XB D F ρ A ∂ ρ ⋅ ∂ P A ZG d, m F + C XB D D B ∂ C ⋅ ∂ M D m d, m G ∂ M ⋅ ∂ P G d, m Equation 6.4-3 m ZG d, m Equation 6.4-4 The drag coefficient variation with Mach number and incidence is determined using central differences with (∆Mm := 0.05; ∆σm := 0.5°). The drag variation with speed, ∂ F ∂ P& XB D G d, m : = 2 ⋅ F XB ⋅ P& XB ⎛ ( ) ⎟ ⎟ D d, m D ⎜ D B D m + ⋅ ⋅ + ⋅ 2 ⎜ MV G G P& CD ∂ ξB ∂ P& ∂ Mm ∂ P& d, m G F ⎝ ∂ C ∂ ξ MV d, m ∂ C ∂ M Equation 6.4-5 The drag variation with missile body orientation with respect to LGA, ∂ F XB D B G ∂ Q : = XB D F C D ⋅ ∂ C ∂ ξ D MV B ∂ ξ ⋅ ∂ Q MV B B G d, m ⎞ ⎠ Equation 6.4-6 The missile body incidence variation with velocity and orientation are defined in §16,16. The remaining gradients are defined in §19.3. 6.5 Missile Guidance - Proportional Navigation 6.5.1 Historical Perspective The first published assessments of Pure Proportional Navigation (PPN) and True Proportional Navigation (TPN) apply linear analysis to the relative missile and target motion in the plane containing their constant velocity vectors. The solution of the highly non-linear PN equations has been a fruitful area of research and one that has taken time even for the simplest cases involving non-manoeuvring targets. The constant speed limitation of these initial analyses has gradually been eroded. Generalised of TPN and PPN laws have to a great extent seen a unification in the analysis however, the purely analytical approach has largely been superseded by optimal LQR techniques as more flexibility has been added. This review charts the evolution of PN guidance laws.
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CRANFIELD UNIVERSITY LEIGH MOODY SE
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ABSTRACT When considering advances
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Contents _ _ LIST OF CONTENTS 1 INT
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Contents _ _ 8.2 The Scope of Moder
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Contents _ _ 17.4 Inertial Velocity
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Tables _ _ LIST OF TABLES Table 1-1
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Figures _ _ LIST OF FIGURES Figure
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Figures _ _ Figure 5-1 : Centralise
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Figures _ _ Figure 19-3 : Air Densi
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Acronyms _ _ Acronyms And Abbreviat
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Acronyms _ _ HDOP - NAVSTAR GPS Hor
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Acronyms _ _ RCS - Radar Cross Sect
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Glossary _ _ GLOSSARY A challenge w
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Glossary _ _ 0.1 Predicate Calculus
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Glossary _ _ ]A,B] Real number rang
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Glossary _ _ 0.9 Matrix Operators [
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Glossary _ _ 0.14.2 Special Vectors
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Glossary _ _ P C a , b ≡ XC YC ZC
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Glossary _ _ V ≡ V : = V • V Th
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Glossary _ _ 0.16.4 Matrix Partitio
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Glossary _ _ Only the subset of qua
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Glossary _ _ 0.19 Systeme Internati
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1 Chapter 1 / Introduction _ _ Chap
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Chapter 1 / Introduction _ _ Wherea
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Chapter 1 / Introduction _ _ • Cr
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Chapter 1 / Introduction _ _ genera
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Chapter 1 / Introduction _ _ radar
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Chapter 1 / Introduction _ _ simple
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Chapter 1 / Introduction _ _ optimi
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Chapter 1 / Introduction _ _ 1.3.9
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2 Chapter 2 / Target Modelling _ _
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Chapter 2 / Target Modelling _ _ 2.
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Chapter 2 / Target Modelling _ _
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Chapter 2 / Target Modelling _ _ t
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Chapter 2 / Target Modelling _ _ P&
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Chapter 2 / Target Modelling _ _ GO
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Chapter 2 / Target Modelling _ _ th
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Chapter 2 / Target Modelling _ _
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Chapter 2 / Target Modelling _ _ VX
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Chapter 2 / Target Modelling _ _ ma
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3 Chapter 3 / Sensors _ _ Chapter 3
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Chapter 3 / Sensors _ _ 3.1 Simulat
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Chapter 3 / Sensors _ _ Table 3-4 :
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Chapter 3 / Sensors _ _ Reference D
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Chapter 3 / Sensors _ _ 3.2-9 s s i
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Chapter 3 / Sensors _ _ 3.2-11 t o
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Chapter 3 / Sensors _ _ Figure 3-5
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Chapter 3 / Sensors _ _ Table 3-7 :
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Chapter 3 / Sensors _ _ IF ϕ LIM
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Chapter 3 / Sensors _ _ The phase e
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Chapter 3 / Sensors _ _ Taking expe
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Chapter 3 / Sensors _ _ Expressing
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Chapter 3 / Sensors _ _ INPUT; AA,
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Chapter 3 / Sensors _ _ The functio
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Chapter 3 / Inertial Navigation _ _
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Chapter 3 / Sensors / Gyroscopes _
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Chapter 3 / Sensors / Accelerometer
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Chapter 3 / Sensors / Barometric Al
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Chapter 3 / Sensors / Barometric Al
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Chapter 3 / Sensors / Radar Altimet
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Chapter 3 / Sensors / Radar _ _ 3.8
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Chapter 3 / Sensors / Radar _ _ LF
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Chapter 3 / Sensors / Radar _ _ ( )
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Chapter 3 / Sensors / Radar _ _ S :
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Chapter 3 / Sensors / Radar _ _ SN
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Chapter 3 / Sensors / Radar _ _ 2
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Chapter 3 / Sensors / Radar _ _ ⎛
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Chapter 3 / Sensors / Seeker _ _ 3.
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Chapter 3 / Sensors / Seeker _ _ 5
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Chapter 3 / Sensors / Seeker _ _
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Chapter 3 / Sensors / Seeker _ _ th
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Chapter 3 / Sensors / Seeker _ _ Th
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Chapter 3 / Sensors / Seeker _ _ Th
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Chapter 3 / Sensors / Fins _ _ 3.10
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Chapter 3 / Sensors / Fins _ _ thro
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Chapter 3 / Sensors / NAVSTAR GPS _
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Chapter 3 / Sensors / Helmet Mounte
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Chapter 3 / Sensors / Helmet Mounte
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Chapter 3 / Sensors / Air Data Syst
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Chapter 4 / Target Tracking _ _ 3.1
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Chapter 4 / Target Tracking _ _ Ine
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Chapter 4 / Target Tracking _ _ ran
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Chapter 5 / Missile State Observer
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Chapter 7 / Missile Trajectory Opti
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8 Chapter 8 / Simulation _ _ Chapte
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Chapter 8 / Simulation _ _ 8.1 The
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Chapter 8 / Simulation _ _ 8.3 The
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Chapter 8 / Simulation _ _ Having p
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Chapter 8 / Simulation _ _ 8.5.1 Gl
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Chapter 8 / Simulation _ _ (1) CONS
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Chapter 8 / Simulation _ _ 8.6.2 Ou
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Chapter 8 / Simulation _ _ The file
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Chapter 8 / Simulation _ _ • The
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Chapter 8 / Simulation _ _ comprehe
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Chapter 8 / Simulation _ _ WIN_RATE
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Chapter 8 / Simulation _ _ for this
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Chapter 8 / Simulation _ _ with the
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Chapter 8 / Simulation _ _ Figure 8
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Chapter 8 / Simulation _ _ Table 8-
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Chapter 8 / Simulation _ _ 8.8 Disc
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9 Chapter 9 / Performance _ _ Chapt
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Chapter 9 / Performance _ _ 9.1 Air
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Chapter 9 / Performance _ _ XM ( >
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Chapter 9 / Performance _ _ 9.3 PN
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Chapter 9 / Performance _ _ The eff
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Chapter 9 / Performance _ _ VXMVOM
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Chapter 9 / Performance _ _ VXMVOM
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Chapter 9 / Performance _ _ 9.4 CLO
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Chapter 9 / Performance _ _ AR_BOM
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Chapter 9 / Performance Chapter 9 /
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Initially the position error falls
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values of CN are not always a relia
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crude initialisation introduces err
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9.5.3 Singer Filter Tuning The Sing
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9.6.2 CLOS Study The CLOS study sho
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Chapter 10 / Conclusions _ _ 10-2
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Chapter 10 / Conclusions _ _ 10.3 T
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Chapter 10 / Conclusions _ _ 10.7 M
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Chapter 11 / Future Research _ _ 11
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Chapter 11 / Future Research _ _
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Chapter 11 / Future Research _ _ To
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References _ _ B.4 BAZARAA M.S., SH
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References _ _ F.1 FOX J.E., “A C
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References _ _ H.5 #HULL D.G., RADK
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References _ _ L.2 LOOZE D.P., HSU
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References _ _ N.4 NABAA N., BISHOP
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References _ _ R.3 RUSNACK I., “O
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References _ _ S.15 SINGER R.A.,
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References _ _ Y.2 YUAN P., CHERN J
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Bibliography _ _ B.13 BABA Y., YAMA
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Bibliography _ _ B.40 BECKER J.C.,
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Bibliography _ _ C.33 CORTINA E., O
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Bibliography _ _ E.8 ERSHOV A.A.,
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Bibliography _ _ G.34 GUTMAN P., VE
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Bibliography _ _ H.35 HUSSAIN A.M.,
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Bibliography _ _ K.14 KATZIR S., CL
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Bibliography _ _ L.19 LEFAS C.C,
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Bibliography _ _ M.16 MAYNE D.Q., P
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Bibliography _ _ P.1 PAINTER J.H.,
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Bibliography _ _ R.32 RONG LI X., Z
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Bibliography _ _ S.47 SPEYER J.L.,
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Bibliography _ _ V.5 VIAN J.L., MOO
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Bibliography _ _ W.29 WATSON G.A.,
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Appendix A / Geometric Points _ _ 1
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Appendix A / Geometric Points _ _ 1
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Appendix B / Frames of Reference _
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Appendix C / Axis Transforms _ _ 16
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Appendix C / Axis Transforms _ _ YP
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Appendix C / Axis Transforms _ _ B
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Appendix C / Axis Transforms _ _ YB
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Appendix C / Axis Transforms _ _ Us
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Appendix C / Axis Transforms _ _ No
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Appendix C / Axis Transforms _ _ B
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Appendix C / Axis Transforms _ _
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Appendix D / Point Mass Dynamics _
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Appendix E / Earth Geometry _ _ 18-
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Appendix E / Earth Geometry _ _ ELL
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Appendix E / Earth Geometry _ _ (dx
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Appendix E / Earth Geometry _ _ Int
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Appendix E / Earth Geometry _ _ 18.
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Appendix E / Earth Geometry _ _ 19-
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Appendix E / Earth Geometry _ _ P S
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Appendix E / Earth Geometry _ _ 19.
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Appendix E / Earth Geometry _ _ ∂
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Appendix G / Gravity _ _ 20-2
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Appendix G / Gravity _ _ g : = g +
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Appendix G / Gravity _ _ d −6 2
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Appendix G / Gravity _ _ 20-8
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Appendix H / Steady State Tracking
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Appendix I / Utilities _ _ 22.1-2
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Appendix I / Utilities _ _ Cartesia
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Appendix I / Utilities _ _ Matrix P
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Appendix I / Utilities _ _ 22.1-8
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Appendix I / Utilities / General Ut
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Appendix I / Utilities / WGS 84 Tar
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Appendix I / Utilities / Axis Trans
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Appendix I / Utilities / Point Mass
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Appendix I / Utilities / Earth, Atm
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Appendix I / Utilities / Earth, Atm
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Appendix I / Utilities / Digital Ma
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Appendix I / Utilities / Digital Fi
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Appendix I / Utilities / Matrices _
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Appendix I / Utilities / Quaternion
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Appendix I / Utilities / Trigonomet
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Appendix I / Utilities / Vectors _
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Appendix I / Utilities / Covariance
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