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Variational modal identification of gyroscopic distribution parameter systems is discussed. Topics covered include: equation of motion for gyroscopic distributed-parameter systems; a variational formulation for the eigenvalue problem; a variational formulation for the modal identification of gyroscopic distributed-parameter systems; discretization; and numerical example.
The gyroscopic instruments commonly used in instrument flying in the United States are the turn indicator, the directional gyro, the gyromagnetic compass, the gyroscopic horizon, and the automatic pilot. These instruments are described. Performance data and the method of testing in the laboratory are given for the turn indicator, the directional gyro, and the gyroscopic horizon. Apparatus for driving the instruments is discussed.
Gyroscopic cross coupling between pitch and yaw was simulated with a variable-stability helicopter while hovering in a yawing maneuver to ascertain the effect of cross coupling on handling qualities. Pilot ratings of the controllability of cross coupling were obtained for various combinations of longitudinal control power, angular velocity about the yaw axis, and simulated engine angular momentum. A theoretical investigation, supplemented by simulator data, was undertaken to determine the effect of longitudinal damping on the coupling controllability. Also, a comparison was made between flight and simulator data. The results indicated that for an aircraft with otherwise satisfactory longitudinal handling qualities, the level of cross coupling is satisfactory when less than 30 percent of the available longitudinal control will trim out the largest gyroscopic coupling moment which might be encountered. Increased longitudinal damping resulted in a significant increase in the controllability of pitch-yaw gyroscopic cross coupling.
A potential application of a superfluid gyroscope is for real-time measurements of the small variations in the rotational speed of the Earth, the Moon, and Mars. Such rotational jitter, if not measured and corrected for, will be a limiting factor on the resolution potential of a GPS system. This limitation will prevent many automation concepts in navigation, construction, and biomedical examination from being realized. We present the calculation of thermal and quantum-mechanical phase noise across the Josephson junction of a superfluid gyroscope. This allows us to derive the fundamental limits on the performance of a superfluid gyroscope. We show that the fundamental limit on real-time GPS due to rotational jitter can be reduced to well below 1 millimeter/day. Other limitations and their potential mitigation will also be discussed.
This paper reports on JPL's on-going research into MEMS gyroscopes. This paper will describe the gyroscope's fabrication-methods, a new 8-electrode layout developed to improve performance, and performance statistics of a batch of six gyroscopes recently rate tested.
We analyze the effect of a highly dispersive element placed inside a modulated optical cavity on the frequency and amplitude of the modulation to determine the conditions for cavity self-stabilization and enhanced gyroscopic sensitivity. Hence, we model cavity rotation or instability by an arbitrary AM/FM modulation, and the dispersive element as a phase and amplitude filter. We find that anomalous dispersion may be used to self-stabilize a laser cavity, provided the magnitude of the group index of refraction is smaller than the phase index of refraction in the cavity. The optimal stabilization is found to occur when the group index is zero. Group indices with magnitudes larger than the phase index (both normal and anomalous dispersion) are found to enhance the sensitivity of a laser gyroscope to rotation. Furthermore, our results indicate that atomic media, even coherent superpositions in multilevel atoms, are not useful for these applications, because the amplitude and phase filters work against one another, i.e., decreasing the modulation frequency increases its amplitude and vice versa, with one exception: negative group indices whose magnitudes are larger than the phase index result in negative, but enhanced, beat frequencies. On the other hand, for optical resonators the dispersion reversal associated with critical coupling enables the amplitude and phase filters to work together under a greater variety of circumstances than for atomic media. We find that for single over-coupled resonators, or in the case of under-coupled coupled-resonator-induced absorption, the absorption and normal dispersion on-resonance increase the contrast and frequency of the beat-note, respectively, resulting in a substantial enhancement of the gyroscopic response. Moreover, for cavity self-stabilization, we propose the use of a variety of coupled-resonator induced transparency that is accompanied by anomalous dispersion.
We propose a tuning method for Micro-Electro-Mechanical Systems (MEMS) gyroscopes based on evolutionary computation that has the capacity to efficiently increase the sensitivity of MEMS gyroscopes through tuning and, furthermore, to find the optimally tuned configuration for this state of increased sensitivity. We present the results of an experiment to determine the speed and efficiency of an evolutionary algorithm applied to electrostatic tuning of MEMS micro gyros. The MEMS gyro used in this experiment is a pyrex post resonator gyro (PRG) in a closed-loop control system. A measure of the quality of tuning is given by the difference in resonant frequencies, or frequency split, for the two orthogonal rocking axes. The current implementation of the closed-loop platform is able to measure and attain a relative stability in the sub-millihertz range, leading to a reduction of the frequency split to less than 100 mHz.
We describe a gyroscope that measures rotation based on the effects of the rotation on the polarization of light. Rotation induces a differential phase shift in the propagation of left- and right-circularly polarized light and this phase shift can be measured in suitably designed interferometric setups. The signal in this setup is independent of the frequency of light, unlike various sources of noise such as vibrations, which cause phase shifts that depend on the frequency. Such vibrations are the practical limit on the sensitivity of conventional Sagnac-style optical interferometers that are typically used as gyroscopes. In the proposed setup, one can potentially mitigate this source of noise by simultaneously using two (or more) sources of light that have different frequencies. The signal in this setup scales with the total storage time of the light. Due to its frequency independence, it is thus most optimal to measure the signal using superconducting radio-frequency systems where the high finesse of the available cavities enables considerably longer storage times than is possible in an optical setup.
Langevin dynamical simulations are performed to investigate the formation of clusters and voids of a two-dimensional periodic substrate (2DPS)-modulated two-dimensional dusty plasma (2DDP) driven by a gyroscopic force. It is discovered that, as the frequency of the gyroscopic force decreases gradually, the substrate-modulated 2DDP undergoes the cyclic transition between the ordered cluster and void phases. Between the observed ordered cluster and void phases, the studied 2DDP exhibits a more uniform arrangement of particles. The discovered cyclic transition is attributed to the symmetry of the time-averaged potential landscape induced by the 2DPS in the reference frame of the moving particle, as confirmed by superimposing the particle locations on the effective potential landscape under various conditions.
Schiff gyroscope experiment as test of Brans- Dicke scalar tensor general relativity theory, deriving expression for gyroscope momentum precession
Test methods and results are presented for the equivalent average input rate of a single-degree-of-freedom gyroscope operated both open loop and with a ternary-logic pulse-torque-to-balance loop during multiaxis angular oscillation. For the open-loop tests, good agreement was obtained with theoretical results. Two-axis testing was performed for oscillations about the Input-Output axes, the Input-Spin axes, and the Spin-Output axes. These tests run in the torque-to-balance mode revealed significant departures from open-loop results in the induced drift rate. An analysis is developed explaining much of the closed-loop data presented. Test data for the gryoscope in a ternary torque-to-balance loop with constant input rates is presented. The tests demonstrate that the instrument rate linearity does not change with interrogation frequency from 3,600 to 14,400 Hz if the torque coil is tuned to offer a resistive load to the current switch. Analysis cited shows that gyroscope lag compensation eliminates multiple pulsing and other equivalent forms of degraded resolution in a wide variety of quantizing loops. This result is test verified for the ternary delta-modulator loop.
A new width modulated pulse rebalance electronics loop was developed for use with strapdown gyroscopes. Advantages of the width modulated binary over the ternary loop are the following: (1) The H-switch is easier to implement; (2) torque is applied in finely quantized increments; (3) the analog-to-digital conversion for data generation is inside the loop and is directly determined by the torque pulse; (4) on part of the loop compensation network bypasses the gyroscope; and (5) the torquer is fed constant power.
Magnetic flux trapped in the rotor of a superconducting gyroscope can cause the rotor to lose energy through dissipation in a readout loop encompassing the rotor and by the generation of eddy currents in the support electrodes. These losses are calculated and shown to be negligible for the rotor in the gyroscope-relativity experiment, a proposed satellite experiment which is to test predictions of the theory of general relativity.
A gyroscope for verifying certain predictions of General Relativity is under development at Stanford. A method of measuring the gyroscope orientation based on the use of the London moment and a SQUID magnetometer is described. It is estimated that the required sensitivity of 1 milliarc-sec can be achieved in a bandwidth of 2.5 times 10 to the -6th Hz.
We demonstrate that for a large class of Lagrangian-based torsion theories a macroscopic gyroscope is insensitive to the torsion field: there can be no coupling of the torsion to the gyroscope's angular momentum of rotation. To detect torsion a polarized system with a net elementary particle spin is needed. These conclusions are evident from the conservation laws, which form the basis for deriving the equations of motion.
This paper discusses an error analysis for the Stanford Relativity experiment, designed to measure the precession of a gyroscope's spin-axis predicted by general relativity. Measurements will be made of the spin-axis orientations of 4 superconducting spherical gyroscopes carried by an earth-satellite. Two relativistic precessions are predicted: a 'geodetic' precession associated with the satellite's orbital motion and a 'motional' precession due to the earth's rotation. Using a Kalman filter covariance analysis with a realistic error model we have computed the error in determining the relativistic precession rates. Studies show that a slightly off-polar orbit is better than a polar orbit for determining the 'motional' drift.
Four basic areas of research and development of superconducting gyroscopes are studied. Chapter 1 studies the analysis of a SQUID readout for a superconducting gyroscope. Chapter 2 studies the dependence of spin-up torque on channel and gas properties. Chapter 3 studies the theory of super fluid plug operation. And chapter 4 studies the gyro rotor and housing manufacture.
The high-resolution gyroscope readout system for the Stanford Gravity Probe-B experiment, whose purpose is to measure two general relativistic precessions of gyroscopes in earth orbit, is described. In order to achieve the required resolution in angle (0.001 arcsec), the readout system combines high-precision mechanical fabrication and measurement techniques with superconducting thin-film technology, ultralow magnetic fields, and SQUID detectors. The system design, performance limits achievable with current technology, and the results of fabrication and laboratory testing to date are discussed.