Index

1 N (spin speed) vibration sensitivity OTG 140 effect on IN system 116 importance of wheel balance 116 SOPG 115

20P (see Two-degree-of-freedom gyro) 2N (twice spin speed) vibration sensitivity

OTG, angular 140 OTG, radial 140

Absorption, fiber 227 Acceleration

centrifugal 91 centripetal 91 Coriolis 90, 133

Acceleration insensitive drift rate 28 Acceleration sensitivity, gyro 34 Acceleration-squared drift rate 35 Accelerex accelerometer 77

bias stability 79 output model 78 signal processing 78

Accelerometer 6, 8, 11 Accelerex 77 angular 38 basic single-degree-of-freedom 44 electrostatic 44 elements 43 fiber optic 55 from SOP gyro 118 Mach-Zehnder 55 micromachined silicon 67 multisensor 164 open loop 46 pendulous 57 pendulous, open loop 48 piezoelectric 43 PIGA 118 Q-F1ex 61

Accelerometer (cont.) scale factor 58 SuperfJex 77 surface acoustic wave 55 VBA72 vibrating beam 75 vibrating string 72

Accelerometer bias, system error 28 Accelerometer testing

"plus/minus Ig" 244 centrifuge 246 in-run bias stability 246

Acceptance Test Procedure (A TP) 40 Acceptance tests 242

accelerometer 243 optical gyros 256 SOP rate gyro 247 SOP rate-integrating gyro 248

Acousto-optic frequency shifter 194 Aiding the lMU 19,261 Aliasing 82 Alignment

gyrocompassing 15 transfer 17

Altitude error, barometer compensated 25 Angle random walk 174 Angular acceleration error 37, 80, 260

model 61 pendulous accelerometer 58 VBA80

Angular accelerometer 38 in autopilot 38 threshold error 38

Angular momentum 85 conservation 92

Anisoelasticity 34, 252 OTG 143 SOP gyro 113 vibrating string gyro 153

Anisoinertia 37, 80,150,260 OTG 144 dynamic 115

Anisoinertia (cont.) frequency dependence 114 model 61 pendulous accelerometer 58 SOF gyro 114 VBA80

Anodic bonding 68 Anti-Shupe winding, IFOG 199 Apollo moon lander 6, 19 Asymmetric damping error, HRG 160 Asymmetry, scale factor 28,61 Attachment, fiber-chip 198 ATP (see Acceptance Test Procedure) Axes transformation 14

Backscatter 234 IFOG 230 MOG234 RFOG229

Ball bearing 95 compared to gas bearing 111 contact angle 113 noise 31,166 output axis 95 rotor 98

Bandwidth 48 muItisensor 166 practical values 50 rate gyro 10 I

Barometric altitude compensation 17, 25 Beam splitter 226 Bearing

angular contact 113 ball 95, 98, III externally pressurized gas !1O friction 87 gimbal 17, 95 journal!11 output axis 104 passive magnetic 110 self-acting gas lubricated III, 128 thrust 112

Beat length 184 Bellows, expansion compensation 107 Beryllium 124, 126

in SOFG gimbal 109 Bias error 28

accelerometer 8, 30 OTG, from damping and mistuning 137 due to damping 153 ESG 128 from bearing vibration 150 from iron inclusion 65 from leakage currents 52 from temperature gradient in IFOG 199 from timing errors 52

Bias error (cont.) gyro 28 Kerr effect 202 magnetic 66 measurement 254 stability, Accelerex 79 tuning fork mass shift 155 VBA80 vibrating cylinder gyro 163

Bias instability from optical fiber aging 33 in laser gyros 33

Binary feedback 51 Birefringence 184,226 Bragg cell 195, 225

MOG232 Bryan, G.H. 158

Capacitive pickoff 62 Center of percussion 63

Index 269

Central Inertial Guidance Test Facility 239 Centrifuge sensor test 242, 246 Closed- versus open-loop sensors 50 Coherence

length 230 oscillator 185

Coherent propagation through a fiber 188 Coil winding, IFOG 199 Common mode rejection

passive ring resonator 226 Comparison of RFOG, IFOG, and MOG 235 Compass, magnetic 4, 5 Compensation

Coriolis acceleration 90 temperature 59, 64

Compensator damping 96, 98, 102, 107 volume 107

Compliance, spring 35 Composite error 27 Contact angle, ball bearing 113 Coordinated Universal Time 4 Coriolis acceleration 90,153, 164 Creep 109

vibrating string accelerometer 74 Critical angle 182 Critical damping 46 Cross-anisoelastic error 114 Cross-coupling 48

coefficient 60 due to hinge 59 error 48, 62, 78, 100 torque 49

Cross-track error distance 25 from angular accelerometer 39

270 Index

Cryogenic 2DF gyro 126

D'Arsonval torquer 102,124 Damping

critical46 electrical, in SDFG 107 fluid 98 mechanical compensator 98 rate gyro 98 squeeze film 63, 69, 77, 124 temperature compensation 1 (Jl

viscous shear 98, 106 DART (Dual Axis Rate Transducer)

construction 166 error sources 166

Day-to-day uncertainty 33 Dead band 32 Deduced (dead) reckoning 4, 6 Demodulation 164 Design check lists 265 Detector 225, 228

surface mounted 232 Diamond pivot 66 Differential design 262 Digital phase ramp 198 Diode

edge-emitting LED 192 laser, chirped 193 superluminescent 192

Diode laser, construction 211 Direction cosines 14 Displacement hysteresis test 248 Distance error

cross-track 25 from accelerometer scale factor 30 from gyro bias 31

Doppler ground speed measurement 5 Doppler shift 195 Drift

GPS satellite 21 in inertial platform 19 asymmetric damping, HRG 160

Dry tuned gyro (see DTG) 131 DTG (Dynamically tuned gyro) 131

IN error 140 2N errors 140 anisoelasticity 143 anisoinertia 144 damping and time constant 137 elastic restraints 138 figure of merit 136 model equation 149 nutation 136 pickoff 146 pseudoconing 145 quadrature mass unbalance 139

DTG (cont.) rate testing 256 sources of 2N vibration 142 synchronous vibration rectification 140 testing 253 time constant 137 torquer 147 torquer magnet 149 tuning equations 132

Dual Axis Rate Transducer (DART) 166 Dynamic inertia 131 Dynamic negative spring 134 Dynamic range

accelerometer 22 for open-loop sensor 51 gyroscope 14, 17

Dynamically Tuned Gyro (see DTG) 131

Earth, shape 6, 9 Earth's rate

horiwntal7 vertical 7

Edge-emitting LED 192 Eight-position test 254 Elastic restraint, DTG 138 Elastic modulus vs. temperature 75,138,161 Electrically suspended gyro (ESG) 126 Electrostatic forcer 66 ElgiJoy rate gyro torsion bar 100 Emission

spontaneous 209, 235 stimulated 209

Environmental test equipment 241 Equation of motion 28

spinning body 89 Equatorial tumble test 251 Error analysis 25 ESG (Electrically suspended gyro)

construction 126 drift performance 128 mass unbalance modulation 127

Etalon 176 Ether, properties 169 External gimbal two-axis gyro 123

Fabry-Perot resonator 176, 212 etalon 176 figure of merit 181 finesse 179 free spectral range 178 frequency response 178

Failure rate 264 Faraday effect 256 Faraday rotator 217 Fatigue life, silicon 67

Feedback binary 51 effect on sensors 53 ternary 53 width-modulated binary 52

Fiber attachment to chip 198 beat length 184 birefringent 184 coherent propagation 188 h-parameter 184 optical 181, 183

Fiber optic accelerometer 55 gyro, interferometric (lFOG) 188 gyro, resonant (RFOG) 227

Fiber-to-chip alignment 198 Figure of merit

DTG 136 optical resonator 181, 228 ring resonator 181

Finesse 179 fiber resonator 228 RLG 217, 219-221

Aexlead 66,100,103, 124 Aoat 105 Aotation 95, 105, 124 Aotation fluid 106, 107

brominated 108 fluorocarbon 107 silicone 108

Auid, flotation 106, 107 Aux valve II Forcer 43

electrostatic 66, 67 inductance 65 magnet stability 59 moving magnet 66 optimum air gap 65

Foucault pendulum 85, 153 Foucault, Leon 85,122 Free spectral range (FSR) 178 Frequency shifter 228, 229

acousto-optic 194, 225 Bragg 195 SAW 231 serrodyne 197, 229

Fresnel drag 214 Fundamental limit

IFOG202 mechanical gyro 174 MOG233 optical gyros 174 passive ring resonator 227 RLG220

Gain curve, Ne 210, 217

Gallium aluminum arsenide 211 Gas bearing

cross-anisoelasticity 114 externally pressurized 110 free (2DF) gyro 128 materials 112 SDFG wheel III

Index 271

Geophysical passive ring resonator 227 Gimbal

floated 105 in inertial platform 8 rate gyro 95

Gimbal lock 12 Global Positioning System (GPS) II, 20 GLONASS satellite navigation system 20 GMT (Greenwich Mean Time) 4 GPS (Global Positioning System) 12,20

and GLONASS in one receiver 21 for mapmaking 21

GPS/INS hybrid navigator 22 Gravity

gradiometer 9, 260 modeling variation over the earth 8 plumb bob 8 standard 8

Green chart 256 Greenwich Mean Time 4 Guided wave optics 195 Gyro 8, 85

bias 28 dynamic range 14 dynamically tuned (tuned rotor) 131 electrically suspended 126 external gimbal, 2DF 123 floated,2DF 124 floated, SDF 105 gain, SDFG 104 gas bearing free rotor 128 hemispherical resonator (HRG) 159 IFOG 188 multi sensor 164 passive ring resonator 225 performance dependencies 266 rate 95 RLG208 silicon, micromachined 156 single-degree-of-freedom 92 spherical free rotor 125 superconductor 126 tuning fork 154 two-degree-of-freedom 11,92 vibrating cylinder 162 vibrating shell 158 vibrating string 153

Gyro bias for gyrocompassing 17 Gyro test labs 239

272 Index

Gyro test labs (contd.) Holloman 240

Gyro test stand rate table 240 servo table 240

Gyro testing 239 angle random walk 256 dithered RLG 256 DTG rate testing 256 dynamically tuned gyro 253 eight -position test 254 g-sensitive terms 251 high-rate scale factor 252 in-run random drift 249 low-rate torquer scale factor 250 optical gyros 256 polar axis test 251 SDF rate gyro 247 six-position test 249 tombstone 249 vibrator for higher-order terms 252

Gyrocompass 5 Gyrocompassing 15

strapdown 16

h-parameter, fiber 184 H-switch 52 Heading and attitude, defined by gimbals 11 Heading and Attitude Reference Systems

(HARS) 11 Heading error, effect on navigation 25 Helium-neon laser 210 Hemispherical Resonator Gyro (HRG) 159 Hinge

diamond pivot 66 pendulous accelerometer 59 stress 58

Hooke's joint 131 HRG (hemispherical resonator gyro)

asymmetric damping error 160 construction 159 node precession 160 performance 158 Q-factor 160 scale factor 160 time constant 160

Hunt, spin motor 114 Hypervelocity projectile 163 Hysteresis 33, 243

DTG flexure 137 magnetic 66 measurement 247 mechanical 50 silicon 67

Hysteresis motor 97, 114 Ice skater 92

IEEE model equation accelerometer 243 accelerometer asymmetry 61 DTG 149,253 pendulous accelerometer 60 RLG 222,257 SDF rate-integrating gyro 117 SDFG248

IEEE standards 25 IFOG (Interferometric Fiber-Optic Gyro)

n/2 bias 190 all-fiber 193 bias from temperature gradient 199 closed loop 194 coil winding 199 digital phase ramp 198 Faraday effect 201 fiber to chip attachment 198 fundamental limit 202 Kerr effect 20 I light source 192 minimum configuration 193 NASNCalTech JPL 198 open loop 189 open-loop range 189 phase nulling 194 piezoelectric biasing 191 polarization-induced bias 201 Rayleigh backscattering 192 reciprocity 193 serrodyne 197 shot noise limit 203 Shupe effect 199

In-run drift 31 Induction motor 126 Inertia

dynamic 131 polar 94

Inertial measurement unit (IMU) 8 Inertial memory 163,263 Inertial navigation 6

applications 22 process 8 system 8

Inertial platform cryogenic 126 single axis 9 three-axis 11 two-axis 122

Inertial property of light 169 Inertial reference unit 8 Inertial sensors 8 Input axis 27 INS/GPS hybrid navigator 22 Integrated optics 195, 196,229,234

MOG231

Interferometer Fabry-Perot 176 ~ach-Zehnder55, 175 multiple beam 175 ring 170 Sagnac 175, 185 single-beam 175

Ion exchange 232 Interferometric Fiber-Optic Gyro (see IFOG)

Kearfott, VBA 79 Kerr effect 237

electro-optic 20 I, 229 in IFOG 201 in ~OG234 in RFOG 227 magneto-optic 216

Langmuir flow 214 Laser 208

diode, chirped 193 GaAIAs 230, 234 GaInP 235 helium-neon (HeNe) 210, 225 longitudinal modes 210 quantum well 230 RFOG230 ring 212 semiconductor 211

Law of Gyroscopics 87 LEO (light emitting diode) 192 Light

coherence 185 inertial property 169

Light emitting diode (LEO) 192 Linearity, pickoff 50 Linewidth

and resolution 74 mechanical 47 resonator 230

Lithium niobate 196 Lock-in

passive ring resonator 226 RLG 213 VBA 76, 83

Longitude 4 Longitudinal mode

gas laser 210 number 178

Loran-C 19 Loss

absorption 234 radiation 234 scattering 234 waveguide 234

Low-coherence source 192

~ach-Zehnder accelerometer 55 ~agnesium gimbal ring 124 ~agnet

forcer 62 samarium cobalt 149 torquer 103

~agnetic

compass 4, 5, 11 mirror biasing 215 suspension 11 0

Magnetics, gimbal 17 Maps 6 ~ass unbalance

free (20F) gyro 128 measurement 247, 254 quadrature, OTG 139 SOF gyro 105

~ass unbalance modulation 127 Materials

for rate-integrating SOFG 109 gas bearing 112

Index 273

Mean time between failures (~BF) 40, 264 Mechanical dither (RLG) 213 Mechanical vs. optical gyros 263 Memory, inertial 263 Mercury 166 Metal fatigue in unpowered sensor 50 Micro-Optic Gyro 230 Microbend losses 55 Micromachining 80, 155 Microsyn

pickoff 99 suspension stator 110 torquer 103

Minimum configuration, IFOG 193 Misalignment 250

tilt 30 ~odel equation

OTG 149 RLG 222 SOF gyro 117

Modulator, phase 190 ~OG (~icro-Optic Gyro) 231

backscattered light 234 fabrication 232 frequency shifter 232 fundamental limit 233 Kerr effect 234 laser 234 operation 231 resonator line width 234 serrodyne 232 size limit 235 time-division 232

274 Index

MOG (cont.) waveguide loss 234 waveguides 232

Moment of inertia 86 Motor

hunting 114, 144 hysteresis 97, 114 induction 126, 128 permanent magnet 120

MTBF (Mean time between failures) 243 Multioscillator RLG 217 Multisensor 164

Navigation 6 Navigation platform 8 Negative stiffness, dynamic 134 Newton, Sir Isaac 7 Noise

ball bearing 166 pickoff 49 relative intensity 203 RLG quantization 222 shot 174

Nonreciprocal phase shift, !FOG 190 thermal 199

Null electrical and mechanical 50 stability 100

Nutation 89 damping 90 DTG 136 frequency 90 frequency, 2DF gyro 124 frequency, ESG 127 spinning top 88

Oil, rotor bearing 98 Omega navigation aid 19 Open loop

versus closed-loop sensors 50 IFOG 189 sensors 51

Optical fiber 55,181 aging 33 beat length 201 chip attachment 198 fabrication 183 h-parameter 184 monomode 183 single- and multimode 183

Optical pickoff 66 Optical resonator 175

Fabry-Perot 176,212 Figure of merit 181 finesse 179

Optical resonator (cont.) Sagnac effect 175 waveguide 177

Optical vs. mechanical gyros 263 Optics, guided wave 195 Optimum coupling, passive resonator 228 Oscillator coherence 185 Output axis bearing

gyroscopic load 104 magnetic suspension 11 0 SDFG 104

Output model Accelerex 78 VBA80

Paddle damping 106 Parasitic torque 87 PARR (Passive Ring Resonator) 225

fiber optic 227 fundamental limit 227 geophysical, very large 226 lock-in 226 poor common mode rejection 226 stress birefringence 226 transverse modes 225

Path length control, RLG 214 Pendulosity 37, 57 Pendulous accelerometer

compared to VBA 82 hinge 59 pickoff 59 Q-F1ex 61 scale factor 58 silicon, micromachined 67

Pendulous Integrating Gyro Accelerometer (PIGA) 30, 118

Pendulum, Foucault 85,153 Performance dependencies, gyros 266 Permanent magnet 62

aging 82 demagnetization curve 65 motor 120

Perry, John 93 Phase nulling 194 Phase reference 166 Phase shifter

nonreciprocal 190 Photodetector, silicon 66 Photolithography 69, 76, 155,232 Photon shot noise 174 Pickoff 48, 96

capacitive 62, 67,124,129, 160 differential transformer 59 DTG 146 in inertial platform 11 linearity 50

Pickoff (coni.) microsyn 99 noise 49 optical 66, 127 piezoresistor 67 potentiometer 123 residual null voltage 146

Piezoelectric 75, 154, 162, 164 IFOG biasing device 191 OA bearings 104 phase modulator 191 RLG dither motor 213 RLG path length control 214 zinc oxide film 232

PIGA (see Pendulous Integrated Gyro Accelerometer)

Platform system vs. strapdown 17, 260 Plus/minus Ig test 244 Polar axis tumble test 251 Polarization 183,225,226

effects in IFOG 201 ion exchanged waveguides 232 temperature 226

Polarization maintaining fiber 200 Population inversion 209 Position error

from accelerometer bias 29 from level tilt 30

Power density in waveguide 229 Precession 87, 88

HRG antinodes 160 rate 88 vibrating cylinder gyro nodes 162

Precision-guided munitions 231 Propagation constant 177 Pseudoconing, DTG 145 Pulse feedback, effect on sensors 53 Pulse torquing 61 Pulse weight 26,51,180,236

RFOG230

Q-factor 47, 81 and resolution 74 HRG 160 magnetic suspension 110

Q-Flex accelerometer 61 Quadrature mass unbalance, DTG 139 Quadrupole winding, IFOG 199 Qualification tests 242 Quantization 256, 258 Quantization noise 222 Quantum limit, RLG 220 Quartz

resonator 75 tuning fork gyro 155

Radio navigation system Global Positioning System 19 Loran-C 19 Omega 19 Transit 19

Random drift 31, 87

Index 275

Random walk 32,174,213,256,258 measurement 258

Rate gyro ball bearings 98 damping 98 dynamics 100 pickoff 99 scale factor 96 single-axis 95 spin motor 97 torque equation 100 torsion bar 100

Rate-integrating gyro 102 anisoelasticity 113 anisoinertia 114 damping 106 definition 103 externally pressurized gas bearing 110 float balancing 105 flotation fluid 107 gain 104 gas spin bearing 111 magnetic suspension 110 materials 109 OA bearing 104 torquer 102 vibration rectification 115

Rayleigh criterion 74 Rayleigh scattering 192,202

backscatter 230 Reaction torque 99 Reciprocity 193 Redundancy 122,264 Reference frame 91

inertial 7 local level 7 of map 6 vehicle axes 7

Reflection, total internal 182 Relative intensity noise 203 Reliability

from redundant sensors 123 mechanisms vs. electronics 13 testing 243

Residual null voltage, DTG pickoff 146 Residuals 244, 252

data processing 27 Resistance-temperature coefficient 65 Resolution 33

measurement 247 vibrating accelerometer 74

276 Index

Resonance, putting to use 262 Resonant frequency, mass-spring 46 Resonator

Accelerex 77 active 181 active and passive types 180 Fabry-Perot 212 Figure of merit 181 optical 175 passive 181 power transmission 177 quartz 75 VBA 79 waveguide 177 waveguide ring 230

RFOG (Resonant Fiber Optic Gyro) 227 high-coherence source 230 Kerr effect 229 laser linewidth 230 multiple tum resonator 229 optimum coupling 228 pulse weight 230 serrodyne frequency shifter 229

Ring laser 212 RLG (ring laser gyro)

construction 214, 216 dithered 213 dynamic balance 213 four-frequency 217 Fresnel drag 214 Langmuir flow 214 lock-in 213 magnetic mirror bias 216 multi oscillator 217 quantization noise 222 quantum limit 220 random walk 213 shared mirror 219 testing 256 typical parameters 221

Rotary transformer 166 noise 166

Rotation-induced errors 36 Rotor balance 116 Run-up and run-down time 98

Sagnac effect 170 magnitude 189 visualization 212

Sagnac interferometer ambiguous output 173 description 171 need for bias 172 polarization 184

Sagnac, Georges 170 Samarium cobalt 149

Scale factor 26 Accelerex 78 accelerometer 30 asymmetry 27, 28, 60, 61, 252 composite error 27 error, gyro 27 gyro, accelerometer 8 measurement 254 multi sensor 166 nonlinearity 27, 234 passive resonator gyro 229 pendulous accelerometer 58 PIGA 119 rate gyro 96 ring interferometer 171 ring resonator 180 standard error 27 VBA80 vibrating cylinder gyro 162 voltage reference limit 54

Scattering, fiber 227 Schuler tuning 12 SDFG testing 240 Self-acting gas bearings III Semiconductor laser 211 Sensor rebalance servos 51 Sensor selection factors 265 Sensor test laboratories 239 Serrodyne frequency shifter

IFOG 197 MOG 232

Servo 44 accelerometer 60 analog 51 binary 51 digital 51 digital; effect on sensor 53 frequency tuning 225 H-switch 52 multirange loop 53 noise 50, 82 overview 51 purpose 50 ternary 53 width-modulated binary 52

Servo table 240 Shannon's theorem 166 Shared-mirror RLG 219 Shock, gun firing 163 Shot noise 235

fundamental limit 173 Shupe effect 199 Sigma plot 256 Signal processing

Accelerex 78 VBA80

Silicon 81

Silicon (contd.) accelerometer 67 fiber connectors 198 gyro, micromachined 156 mechanical properties 67 photodetector 66 waveguides 234

Single-degree-of-freedom gyro (SOFG) 102 Six -position test 249 Slipring 123, 166

in inertial platform 11 noise 166

Smart munitions 163 Specification, typical, for gyro and

accelerometer 40 Spherical free rotor gyro 125 Spinning top 88, 93 Spontaneous emission 235 Spring-mass system

dynamics 44 impulse response 46

Squeeze film 77 damping 63, 69

Standard deviation 249 Standard error 27, 245 Star-tracker 19 START (Solid-State Angular Rate Transducer)

bandwidth 162 construction 162 performance 158 threshold 163

Stiction 32, 82 measurement 248

Stiffness, spring 35 Stimulated emission 208 Strapdown system 8, 13

Apollo 19 axes transformation 14 compared to platform 17, 260 gyrocompassing 16 transfer alignment 17

Structural materials SOF gyro 109

Superconducting gyro 126 Superfluorescent fiber source 193 Superluminescent diode 192, 202 Surface acoustic wave (SAW)

accelerometer 55 frequency shifter 231

Suspension passive magnetic 11 0 stiffness 44

System alignment 15 gyrocompassing 15, 16 star-tracker 19 transfer alignment 16, 17

System error altitude 25 from accelerometer bias 28

Index 277

from accelerometer scale factor 30 from asymmetry 28 from gyro bias 30 from gyro scale factor 27 from level tilt 30

Temperature compensation, magnet 64 operating range 61

Temperature coefficient bias 65 elastic modulus 161 resistance 65

Temperature sensitivity 76 elastic modulus 75 tuning fork gyro 158 vibrating cylinder gyro 163

Ternary feedback 53 Test

acceptance test procedure (A TP) 40 acceptance 242 centrifuge 242, 246 displacement hysteresis 248 eight-position 254 environmental 241 labs, gyro and accelerometer 239 "plus/minus Ig" 244 polar axis (equatorial) tumble 251 six -position 250 tables 240 vibration 253

Testing accelerometers 243 centrifuge 246

Testing gyros OTG253 optical 256 SOF rate gyro 247 SOF rate-integrating gyro 248 tombstone 31, 246

Thermally induced nonreciprocity 199 Three-sigma value 40 Threshold 32

angular accelerometer 38 measurement 247 passive ring resonator 227 vibrating cylinder gyro 163

Tilt misalignment 30 Time, importance in inertial navigation 9 Time constant 75

OTG, definition 137 HRG 160, 163 SOFgyro 107

Time-division, MOG 232

278 Index

Titanium in-diffused waveguide 196 Tombstone test 31, 246 Torque motor, inertial platform II Torquer

d'ArsonvaII02,124 DTG 147 induction 129 microsyn 103 optimum design, DTG 149 rate-integrating gyro 102

Torsion bar 95,100 stiffness 96

Total internal reflection 182 Transfer alignment 16 Transfer characteristics, SDFG 248 Transients, thermal 82 TRANSIT navigation aid 19 Transit time 191 Transmission in a fiber 183 Tumble

"plus/minus 19" 244 polar axis test 249

Tuned rotor gyro (see DTG) 131 Tuning effect, DTG 131 Tuning fork accelerometer 77 Tuning fork gyro 154

quartz 155 silicon micromachined 156

Turn-on stability 39 Two-degree-of-freedom (2DF) gyro 122

ESG 126 external gimbal 123 floated 124 gas bearing 128 spherical 125

U sefullife of a system 264 UTC (Coordinated Universal Time) 4

VBA (vibrating beam accelerometer) 76 Accelerex 77 compared to pendulous accelerometer 82 description 76 Kearfott 79 Kearfott output model 80 lock-in 76 silicon micromachined 80

Velocity error from accelerometer bias 29 from gyro bias 30

Vibrating beam accelerometer, see VBA Vibrating cylinder gyro 162 Vibrating shell gyro 158 Vibrating string accelerometer 72 Vibrating string gyro 153 Vibration

IN,DTG 140 IN, SDFG 115 2N,DTG 140 bearing 150 equation 72 modes, cylindrical shell 158 rectification 76, 115, 140 testing 252

Vibropendulous error 48, 82 definition 48 VBA 77, 80

Viscosity, spin bearing oil 98 Viscous shear damping 98, 106 Voltage controlled oscillator 232 Voltage reference 82 Voltage reference problem 54 Von Braun, Werner 6

Waveguide glass 195 ion exchange 232 lithium niobate 196 loss 234 power density 229 silicon 235 titanium in-diffused 196

Width-modulated binary feedback 52 Winding, quadrupole 199 Wine glass gyro (see HRG) 159

Young's modulus temperature variation 161

Zeeman effect 256 Zero offset 28

Mechanical Engineering Series (continued from page ii)

A Lawrence, Modern Inertial Technology: Navigation, Guidance, and Control, 2nd ed.

R.A Layton, Principles of Analytical System Dynamics

C.V. Madhusudana, Thermal Contact Conductance

D.P. Miannay, Fracture Mechanics

D.P. Miannay, Time-Dependent Fracture Mechanics

D.K. Miu, Mechatronics: Electromechanics and Contromechanics

D. Post, B. Han, and P. Ifju, High Sensitivity Moire: Experimental Analysis for Mechanics and Materials

F.P. Rimrott, Introductory Attitude Dynamics

S.S. Sadhal, P.S. Ayyaswamy, and J.N. Chung, Transport Phenomena with Drops and Bubbles

AA Shabana, Theory of Vibration: An Introduction, 2nd ed.

AA Shabana, Theory of Vibration: Discrete and Continuous Systems, 2nd ed.