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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
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