Index

IN (spin speed) vibration sensitivity DTG 136 effect on inertial navigation system 114 importance of wheel balance 114 SDFG 113

2DF (see Two Degree of Freedom gyro) 2N (twice spin speed) vibration sensitivity

DTG, angular 136 DTG, radial 136

Absorption, fiber 218 Acceleration

centrifugal 90 centripetal 90 CorioHs 89, 130

Acceleration insensitive drift rate 27 Acceleration sensitivity, gyro 32 Acceleration-squared drift rate, gyro 34 Accelerex accelerometer 77

output model 79 signal processing 78

Accelerometer 6, 8, 10 Accelerex 77 angular 38 basic single degree of freedom 43 electrostatic 43 elements 42 fiber optic 55 from SDFG 115 Mach-Zehnder 56 micromachined silicon 67 multisensor 159 open-loop 45 parts of 42 pendulous 57 pendulous, open-loop 47 piezoelectric 42

PIGA 116 Q-Flex 62 scale factor 58 Superflex 78 surface acoustic wave 55 vibrating beam 76 vibrating string 72

Accelerometer bias, system error 27 Accelerometer testing 234

"plus/minus 19" 235 centrifuge 237 in-run bias stability 237

Acceptance Test Procedure (ATP) 39 Acceptance tests 233

accelerometer 234 SDF rate gyro 238 SDF rate-integrating gyro 239

Acousto-optic frequency shifter 188 Aiding the IMU 19,252 Aliasing 81 Altitude error, compensated by barometer 24 Angle random walk 168 Angular acceleration error 35, 80, 251

model 61 pendulous accelerometer 58 VBA 81

Angular accelerometer 38 in autopilot 38 threshold error 38

Angular momentum 84 conservation 85

Anisoelasticity 34, 242 DTG 138 SDFG 110 vibrating string gyro 149

Anisoinertia 37, 80, 146, 251 DTG 140 dynamic 112 frequency dependence 111 model 61

260 Index

Anisoinertia (cont.) pendulous accelerometer 58 SDFG 111 VBA 81

Anodic bonding 69 Anti-Shupe winding, IFOG 192 Apollo moon lander 6, 18 Asymmetric damping error, HRG 155 Asymmetry, scale factor 27,61 Attachment, fiber-chip 191 A TP (see Acceptance Test Procedure) Axes transformation 14

Backscatter 186 RFOG 220 MOG225

Ball bearing compared to gas bearing 109 contact angle 110 noise 31, 160 output axis 93 rotor 96

Bandwidth 47 multisensor 161 practical values 49 rate gyro 99

Barometric altitude compensation 17, 24 Beam splitter 216 Bearing

ball 93,96 friction 87 gimbal 17 journal 110 output axis 102 self-acting gas lubricated 109, 125 thrust 110

Beat length, fiber 178 Bellows, expansion compensation 104 Beryllium 121, 123

in SDFG gimbal 107 Bias error 27

accelerometer 8, 29 DTG, from damping and mistuning 133 due to damping 149 ESG 124 from bearing vibration 146 from iron inclusion 65 from leakage currents 53 from temperature gradient in IFOG 192 from timing errors 53 gyro 8 Kerr effect 194 magnetic 66 measurement 245 tuning fork mass shift 151 VBA 81

Bias instability from optical fiber aging 32 in laser gyros 32

Bias stability, Accelerex 79 Bias temperature sensitivity

vibrating cylinder gyro 156 Binary feedback 51 Birefringence 178, 216 Bragg cell 188,216

MOG 223 Bryan, G.H. 152

Capacitive pickoff 63 Center of percussion 64 Central Inertial Gnidance Test Facility 231 Centrifuge sensor test 232, 237 Check lists, design 256 Closed-loop

accelerometers 49 versus open-loop sensors 50

Coherence length 221 Coherence of an oscillator 179 Coherent propagation through a fiber 182 Coil winding, IFOG 192 Common mode rejection

passive ring resonator 217 Comparison of RFOG, IFOG, and MOG 226 Compass, magnetic 4,5,12 Compliance, spring 34 Composite error 26 Contact angle, ball bearing 110 Coriolis Acceleration 89,149,159 Creep 106

bias in vibrating string accelerometer 73 Critical angle 177 Critical damping 45 Cross-anisoelastic error 111 Cross-coupling

due to hinge 59 error torque 48

Cross-coupling error 47, 63, 78, 97 Cross-track error 24

from angular accelerometer 38 Cryogenic 2DF gyro 122

D'Arsonval torquer 100 Damping

compensator, mechanical 96 critical 45 electrical, in SDFG 104 fluid 96 rate gyro 96 squeeze film 63,69,77, 121 temperature compensation 104

DART (Dual Axis Rate Transducer) construction 160 error sources 160

Day-to-Day uncertainty 32 Dead band 31 Dead (deduced) reckoning 4,6 Demodulation 159

Design check lists 256 Detector 216, 219

surface mounted 223 Diamond pivot 66 Differential design 253 Digital phase ramp 191 Diode

edge-emitting LED 186 laser

chirped 186 construction 202

superluminescent 186 Direction cosines 14 Displacement hysteresis test 239 Distance error

cross-track 24 from accelerometer scale factor 29 from gyro bias 30

Doppler ground speed measurement 5 Doppler shift 189 Dry tuned gyro (see DTG) DTG (Dynamically Tuned Gyro) 127

angular 2N vibration error 137 anisoelasticity 138 anisoinertia 140 axial IN vibration error 136 damping and time constant 132 elastic restraints 134 figure of merit 132 magnet 145 model equation 146 nutation 132 pickoff 142 pseudoconing 141 quadrature mass unbalance 134 rate testing 247 sources of 2N vibration 138 synchronous vibration rectification 136 testing 245 time constant 133 torquer 143 tuning equations 129

Dual Axis Rate Transducer (see DART) 160 Dynamicinertia 127 Dynamic negative spring 130 Dynamic range

accelerometer 21 for open-loop sensor 50 gyroscope 14, 16

Dynamically Tuned Gyro (see DTG)

Earth shape 6, 8 Earth's rate

horizontal 7 vertical 7

Edge-emitting LED 186 Eight position test 245 Elastic modulus, temperature variation 133 Elastic restraint, DTG 134

Index 261

Electrically Suspended Gyro (see ESG) Electrostatic forcer 66 Elgiloy, rate gyro torsion bar 98 Emission

spontaneous 200 stimulated 200

Environmental test equipment 232 Equation of motion 27

spinning body 88 Equatorial tumble test 242 Error analysis 24 ESG (Electrically Suspended Gyro) 123

construction 123 drift performance 124 Mass Unbalance Modulation 124

Etalon 170 Ether, properties 163 External gimbal two-axis gyro 120

Fabry-Perot resonator 170, 202 etalon 170 figure of merit 175 finesse 173 free spectral range 173 frequency response 172

Failure rate 255 Faraday Effect 247 Faraday rotator 209 Fatigue life, silicon 67 Fiber

attachment to chip 191 beat length 178 birefringent 178 coherent propagation 182 h-parameter 178

Fiber optic 177 accelerometers 55 gyro

interferometric, IFOG 182 resonant, RFOG 218

Fiber-to-chip alignment 191 Fibers, optical 175 Figure of Merit

DTG 132 optical resonator 175,219 ring resonator 175

Finesse 173, 208 fiber resonator 219

Flexlead 66,98, 100, 121 Float 103 Flotation 103, 121

fluid 104, 105 brominated 105 fluorocarbon 105 silicone 105

Fluid, flotation 104, 105 Flux valve 12 Forcer 43

electrostatic 66, 67

262 Index

Forcer (cont.) magnet stability 59 moving magnet 66 optimum air gap 65

Foucault pendulum 84,149 Foucault, Leon 84, 119 Free Spectral Range (FSR) 173 Frequency shifter 219,220

acousto-optic 188,216 Bragg 188 SAW 222 serrodyne 190, 220

Fresnel drag 205 FSR (Free Spectral Range) 173 Fundamental limit

IFOG 195 mechanical gyro 168 MOG 224 passive ring resonator 218 RLG 210

Gain curve, Ne 209 Gallium aluminum arsenide 202, 221 Gas bearing

cross-anisoelasticity 111 free rotor gyro 125 materials 110 SDFG wheel 109

Geophysical passive ring resonator 217 Gimbal

floated 103 lock 12 magnetics 17 rate gyro 93

Gimbals in IMU 8 Global Positioning System (see GPS) GLONASS satellite navigation system 19 GPS (Global Positioning System) 1, 19

and GLONASS in one receiver 20 for map making 21

GPS/INS hybrid navigator 21 Gravity variation over the earth 8 Gravity gradiometer 9,251 Green Chart 248 Greenwich Mean Time 4 Guided wave optics 189 Gyro 6,84

dynamic range 14 dynamically tuned (DTG, tuned rotor) 127 electrically suspended (ESG) 123 external gimbal, 2DF 120 floated,2DF 121 gas bearing free rotor 125 hemispherical resonator (HRG) 153 multisensor 159 passive ring resonator 216 rate 93 single degree of freedom (SDF, single axis) 91 spherical free rotor 122

superconductor 122 tuning fork 149 two degree of freedom 10,91 vibrating cylinder 155 vibrating shell 152 vibrating string 149

Gyro bias, for strapdown gyrocompassing 16 Gyro gain, SDFG 101 Gyro test labs 230

Holloman AFB 231 Gyro test stand

rate table 231 servo table 231

Gyro testing 230 dithered RLG 248 DTG 245 eight position test 245 g-sensitive terms 242 high-rate scale factor 243 in-run random drift 240 low-rate torquer scale factor 241 optical gyros 247 polar axis test 242 SDF rate gyro 238 six position test 241 tombstone 240 using vibrator for higher order terms 244

Gyrocompass 5 Gyrocompassing 14

strapdown 15 Gyroscope (see Gyro)

H-parameter, fiber 178 Heading and attitude, defined by gimbals 10 Heading and Attitude Reference System

(HARS) 10 Heading error, effect on navigation 24 Helium-Neon laser 201 Hemispherical Resonator Gyro (see HRG) 153 Hinge

diamond pivot 66 pendulous accelerometer 59 stress 58

Hooke's joint 127 HRG (Hemispherical Resonator Gyro)

asymmetric damping error 155 construction 153 node precession 154 performance 152 Q factor 154 scale factor 154 time constant 154

Hunt, spin motor 111 Hypervelocity projectile 157 Hysteresis 32, 234

DTG flexure 132 magnetic 66 measurement 238 mechanical 49

motor 95, 111 silicon 67

IEEE model equation accelerometer 234 accelerometer asymmetry 61 DTG 146,245 pendulous accelerometer 60 RLG 249 SDF rate-integrating gyro 114,240

IEEE Standards 24 IFOG (Interferometric Fiber Optic Gyro)

n/2 bias 184 all-fiber 187 bias from temperature gradient 192 closed-loop 187 coil winding 192 digital phase ramp 191 Faraday effect 193 fiber to chip attachment 191 fundamental limit 195 Kerr effect 194 light source 186 minimum configuration 187 NASNCalTech JPL 191 open-loop 183 open-loop range 184 phase nulling 187 piezoelectric biasing 185 polarization induced bias 193 Rayleigh backscattering 186 reciprocity 186 serrodyne 190 shot noise limit 195 Shupe effect 192

IMU (Inertial Measurement Unit) cryogenic 123 gimbals 8

In-run drift 31 Induction motor 124 Inertia

dynamic 127 polar 92

Inertial memory 157 navigation 6

applications 21 process 8 system (INS) 8

platform, single axis 9 platform, three axis 10 property of light 163 reference frame 6 reference unit (IRU) 8 sensors 8

INS/GPS hybrid navigator 21 Integrated optics 189, 220, 225

MOG 222 Interferometer

Fabry-Perot 170 Mach-Zehnder 56, 169 multiple beam 170 ring 164 Sagnac 169,180 single beam 169

Interferometric Fiber Optic Gyro (see IFOG)

Ion exchange 223

Kearfott VBA 79 Kerr effect 225, 227

electro-optic 194, 220 in IFOG 194 inMOG 225 in RFOG 218 magneto-optic 206

Langmuir flow 205 Laser 199

diode, chirped 186 GaAIAs 221, 225 GaInP 226 helium-neon (HeNe) 201,216 longitudinal modes 201 quantum well 221 RFOG 221 ring 203 semiconductor 202

Law of Gyroscopics 86 LED (Light Emitting Diode) 186 Light

coherence 179 inertial property 164

Light Emitting Diode (LED) 186 Linearity, pickoff 49 Linewidth

and resolution 73 mechanical 46 resonator 221

Lithium niobate 189 Lock-in

passive ring resonator 217 RLG 203 VBA 76,82

Longitude 4 Longitudinal modes, gas laser 201 Longitudinal mode number 172 Loss

absorption 225 radiation 225 scattering 225 waveguide 225

Low coherence source 186

Mach-Zehnder accelerometer 56 Magnesium gimbal ring 121

Index 263

264 Index

Magnet forcer 63 samarium cobalt 145 torquer 100

Magnetic compass 4, 5, 12 mirror biasing 206 suspension 107

Magnetics, gimbal 17 Maps 6 Mass unbalance 34

free (2DF) gyro 124 measurement 238, 246 quadrature, DTG 134 SDFgyro 104

Mass Unbalance Modulation 124 Materials

for gas bearing 110 for rate-integrating SDFG 106

Mean Time Between Failures (MTBF) 39, 234, 255

Mechanical dither, RLG 203 Mechanical versus optical gyros 254 Mercury 160 Metal fatigue, in unpowered sensor 50 Micro-Optic Gyro (see MOG) Microbend losses 56 Micromachining 81, 151 Microsyn

pickoff 96 suspension stator 108 torquer 100

Minimum configuration, IFOG 186 Misalignment 242 Model equation

SDFG 114 DTG 146 RLG 249

Modulator, phase 184 MOG (Micro Optic Gyro) 222

backscattered light 225 fabrication 223 frequency shifter 223 fundamental limit 223 Kerr effect 225 laser 225 operation 222 resonator linewidth 225 serrodyne 223 size Iimi t 226 time-division 223 waveguide loss 225 waveguides 223

Moment of inertia, definition 85 Motor

hysteresis 95, 111 induction 124, 125 permanent magnet 117

MTBF (Mean Time Between Failures) 39, 234, 255

Multi-oscillator RLG 208 Multisensor

construction 159 principle 157

Navigation 6 Navigation platform 8 Negative stiffness, dynamic 130 Newton, Sir Isaac 6 Noise

ball bearing 160 pickoff 49 RLG quantization 213 shot 168

Non-reciprocal phase shifting 185 Novel accelerometers 54 Null, electrical and mechanical 49 Null stability 98 Nutation

damping 89 DTG 132 frequency 89 frequency, 2DF gyro 121 frequency, ESG 124 spinning top 87

Oil, rotor bearing 96 Open-loop

IFOG 183 pendulous sensors 47 versus closed-loop sensors 50

Optical fiber 55, 175 aging 32 beat length 193 chip attachment 191 fabrication 177 monomode 177 single- and multi-mode 177

Optical gyros versus mechanical 254 Optical pickoff 66 Optical resonator 169

Fabry-Perot 170 figure of merit 174 finesse 173 Sagnac Effect 173 waveguide, two-port 171

Optics, guided waves 189 Optimum coupling, RFOG 219 Oscillator coherence 179 Output axis bearing

gyroscopic load 102 magnetic suspension 107 SDFG 102

Output model Accelerex 79 VBA 80

Paddle damping 104 Parasitic torque 86 PARR (Passive Ring Resonator) 216

fiber optic 218 fundamental limit 218 lock-in 217 poor common mode rejection 217 stress birefringence 216 transverse modes 216 geophysical 217

Passive Ring Resonator (see PARR) Path length control 205 Pendulosity 36, 57 Pendulous accelerometer 57

compared to VBA 81 hinge 59 pickoff 59 Q-Flex 62 silicon micro machined 67 scale factor 58

Pendulous Integrating Gyro Accelerometer (PIGA) 116

Pendulum, Foucault 84, 149 Performance dependencies, gyros 257 Permanent magnet 63

aging 81 motor 117

Perry, John 92 Phase-nulling 187 Phase reference 161 Phase shifter

non-reciprocal 185 Photolithography 69, 76, 151, 223 Photon shot noise 168 Pickoff 94

capacitive 63,67,121,125, 154 differential transformer 59 DTG 142 in inertial platform 10 linearity 49 microsyn 96 optical 66, 124 piezoresistor 67 potentiometer 120 residual null voltage 143

Piezoelectric 76, 149, 155, 157 IFOG biasing device 185 output axis bearings 102 phase modulator 185 RLG dither motor 203 RLG path length control 205 zinc oxide film 223

PIGA (Pendulous Integrating Gyro Accelerometer) 116

Platform system compared to strapdown 16, 251

Plus/minus 19 tumble test 235 Polar-axis tumble test 242 Polarization 178, 216

effects in IFOG 193

Index 265

ion exchanged waveguides 223 temperature 216

Polarization maintaining fiber 192 Population inversion 200 Position error

from accelerometer bias 28 from level tilt 29

Power density in waveguide 220 Precession 86

HRG antinodes 154 rate 88 vibrating cylinder gyro nodes 156

Precision guided munitions 222 Propagation constant 171 Pseudoconing, DTG 141 Pulse torquing 61

effect on sensors 54 Pulse weight 26,51, 174,227

RFOG 221

Q Factor 46 and resolution 73 HRG 154 magnetic suspension 108

Quadrature mass unbalance, DTG 134 Quadrupole winding, IFOG 192 Qualification tests 233 Quantization 248, 249 Quantization noise 213 Quantum limit 210 Quartz

resonator 75 tuning fork gyro 151

Random drift 31,86 Random walk 31,248,249

in angle 168,204 measurement 249

Rate gyro ball bearings 96 damping 96 dynamics 98 pickoff 96 scale factor 94 single axis 93 spin motor 95 torque equation 98 torsion bar 97

Rate-integrating gyro 99 damping 104 definition 100 float balancing 104 flotation 103 gain 101 magnetic suspension 107 materials 106 output axis bearing 102 self-acting gas bearing 109

266 Index

Rate-integrating gyro (cont.) torquer 100 vibration rectification 113

Rayleigh Criterion 73 Rayleigh scattering 186, 194

backscatter 221 Reaction torque 97 Reciprocity 186 Redundancy 119,255 Reference frame 6, 90

inertial 6 local level 7 of map 6 vehicle axes 7

Reliability 254 from redundant sensors 119 from replacing mechanisms with electronics 13 tests 233

Residual, in data processing 26, 236, 243 Residual null voltage, DTG pickoff 143 Resistance temperature coefficient 65 Resolution

definition 31 measurement 238 vibrating accelerometer 73

Resonance, putting to use 253 Resonant Fiber Optic Gyro (see RFOG) Resonant frequency, mass-spring 45 Resonator

Accelerex 77 active 174 active and passive types 174 Fabry-Perot 202 Figure of Merit 174 finesse 173 optical 169 passive 174 power transmission 171 ring 202 VBA 79 waveguide 170, 221

RFOG (Resonant Fiber Optic Gyro) 218 high coherence source 221 Kerr effect 220 laser Iinewidth 221 multiple turn resonator 220 optimum coupling 219 pulse weight 221 serrodyne frequency shifter 220

Ring laser 203 gyro (see RLG) resonators 202

RW (Ring Laser Gyro) construction 204,207 dithered 203 dynamic balance 203 four-frequency 208 Fresnel drag 205 Langmuir flow 205 lock-in 203

magnetic mirror bias 206 mechanical dither 203 multi-oscillator 208 quantization noise 213 quantum limit 210 random walk 204 shared mirror 210 testing 248 typical parameters 212

Rotary transformer noise 160 Rotation induced errors 35 Rotor balance 114 Run-up and run-down time 96

Sagnac effect 164 magnitude 183 visualization 203

Sagnac interferometer 165 ambiguous output 167 need for bias 166 polarization 178

Sagnac, Georges 164 Samarium cobalt 145 SAW (Surface Acoustic Wave) 222 Scale factor 25

Accelerex 79 accelerometer 29 asymmetry 26, 27, 60, 61, 243 composite error 26 error, gyro 26 gyro, accelerometer 8 measurement 246 multisensor 160 non-linearity 26, 225 passive resonator gyro 220 pendulous accelerometer 58 PIGA 117 rate gyro 94 ring interferometer 165 ring resonator 174 standard error 26 VBA 81 vibrating cylinder gyro 156 voltage reference limit 54

Scattering in a fiber 218 Schuler tuning 12 SDFG (Single Degree of Freedom Gyro) 93

rate gyro 93 ball bearings 96 damping 96 dynamics 98 flexlcads 98 pickoff 96 scale factor 94 spin motor 95 torsion bar 97

rate-integrating gyro 99 anisoelasticity 110 anisoinertia 111

damping 104 flotation 103 flotation fluids 105 gain 101 magnetic suspension 107 mass unbalance 104 model equation 114 output axis bearing 102 self-acting gas bearings 109 structural materials 106 torquer 100 vibration rectification 113

testing 231 Self-acting gas bearings 109 Semiconductor laser 202 Sensor rebalance servos 50 Sensor test laboratories 230 Serrodyne frequency shifter 190

forMOG 223 Servo 49

accelerometer 60 analog 50 binary 51 digital 50

offect on sensor 54 frequency tuning 216 H-switch 51 multi-range loop 53 noise 81 overview 50 table 231, 243 ternary 53 width modulated binary 51

Shannon's theorem 161 Shared-mirror RLG 210 Shock, gun firing 157 Shot noise 226

fundamental limit 167 Shupe Effect 192 Sigma plot 248 Signal processing

Accelerex 78 Kearfott VBA 80

Silicon 81 accelerometer 67 fiber connectors 191 mechanical properties 67

Single Degree of Freedom Gyro (see SDFG) Six position test 242 Slip rings 120, 160

in inertial platform 9 noise 160

Smart munitions 157 Solid State Angular Rate Transducer (see

START) Sorg, Helmut 3 Specification, typical, for sensors 40 Spherical free rotor gyro 122 Spin motor

induction 124

hunting 111 hysteresis type 95, 111

Spinning top 87,92 Spontaneous emission 227 Spring-mass system

bandwidth 47 impulse response 45 Q factor 46 system dynamics 43

Squeb iilm 77 damping 63, 69

Standard deviation 39,241 Standard error 26, 236 Star tracker 19

Index 267

START (Solid State Angular Rate Transducer) bandwidth 156 construction 155

"performance 152 threshold 156

Stiction 31, 82 measurement 239

Stiffness, spring 34 Stimulated emission 199 Strapdown system 8, 13

advantages and disadvantages 17 alignment 14 Apollo Lunar Module 18 axes transformation 14 compared to platform 16,251 gyrocompassing 14 transfer alignment 16

Structural materials, SDFG 106 Sundstrand

Accelerex accelerometer 77 Q-Flex Accelerometer 62

Superconducting gyro 122 Superluminescent diode 186, 194 Surface Acoustic Wave (SAW) 222 Suspension

passive magnetic 108 stiffness 44

System alignment 14 gyrocompassing 14,15 star tracker 19 transfer alignment IS, 16

System error from accelerometer bias 27 from accelerometer scale factor 29 from gyro bias 29 from gyro scale factor 26 heading 24

Temperature coefficient

bias 65 elastic modulus 155 resistance 65

compensation, magnet 64 operating range 62

268 Index

TeI!Jperature (cont.) sensitivity 76

elastic modulus 75 t\uning fork gyro 152

Ternal/ feedback 53 Test laboflltories 230 Testing accelerometers 234

centrifuge tests 237 Testing gyros 138

DTG 245 rate testing 247

eight position test 245 optical gyros 247 polar-axis test 242 SDF rate gyro 238 SDF rate-integrating gyro 239 servo table scale factor test 243 sigma plot 248 six position test 241 tombstone tests 240 vibration tests 244

Thermally induced non-reciprocity 192 Three sigma value 39 Threshold 31

angular accelerometer 38 measurement 238 passive ring resonator 218 vibrating cylinder gyro 156

Tilt misalignment 29 Time, importance in IN 9 Time constant 75

DTG, definition 133 HRG 154,157 SDF gyro 105

Time-division, MaG 223 Titanium in-diffused waveguide 189 Tombstone test 30, 237 Torque motor, inertial platform 9 Torquer

d' Arsonval 100 DTG 143 induction 125 microsyn 100 optimum design, DTG 144 rate-integrating gyro 99

Torsion bar 93, 97 stiffness 94

Total internal reflection 177 Transfer alignment 15 Transfer characteristics, SDFG 239 Transients, thermal 82 Transit time 185 Transmission in a fiber 176 Tuned rotor gyro (see DTG) Tuning effect, DTG 127 Tuning fork

Accelerex 77 gyro 149

Tum-on stability 39

Two Degree of Freedom (2DF) gyro 119 gas bearing free rotor 125 electrically suspended (ESG) 123 external gimbal 120 floated 121 spherical free rotor 122

Useful life of a system 255 VBA (Vibrating Beam Accelerometer) 76

compared to pendulous accelerometer 81 Kearfott model 79

signal processing 80 lock-in 76 silicon micromachined 81 Sundstrand Accelerex 77

signal processing 78 Velocity error

from accelerometer bias 28 from gyro bias 29

Vibrating Beam Accelerometer (see VBA) Vibrating cylinder gyro 155 Vibrating shell gyro i52

advantages 157 Vibrating string accelerometer 72 Vibrating string gyro 149 Vibration

equation 72 modes, cylindrical shell 152 rectification 76, 113, 136 tests 244

Vibropendulosity 81 error 47,77

Viscosity, spin bearing oil 96 Viscous shear damping %, 104 Voltage controlled oscillator 223 Voltage reference 81 Voltage reference problem 54 Von Braun, Werner 6

Waveguide glass 189 ion exchange 223 lithium niobate 189 loss 225 silicon 226 titanium in-diffused 189

Width modulated binary loop 51 Winding, quadrupole (IFOG) 192 Wine glass gyro (see HRG)

Young's modulus, temperature variation 155

Zeeman Effect 247 Zero offset 27