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The simplest case of a single electrode is considered. Determination of the mixed boundary condition for this potential leads to dual series equations. Collins' solution to a Fredholm integral equation of the second kind is discussed. This equation is transformed into an infinite set of linear equations from which the coefficients in the dual series equation can be calculated using standard techniques.
The details of implementation of a general numerical procedure developed for the accurate and economical computation of natural frequencies and associated modes of any elastic structure rotating along an arbitrary axis are described. A block version of the Lanczos algorithm is derived for the solution that fully exploits associated matrix sparsity and employs only real numbers in all relevant computations. It is also capable of determining multiple roots and proves to be most efficient when compared to other, similar, exisiting techniques.
This paper describes the details of implementation of a general numerical procedure developed for the accurate and economical computation of natural frequencies and associated modes of any elastic structure rotating along an arbitrary axis. A block version of the Lanczos algorithm is derived for the solution that fully exploits associated matrix sparsity and employs only real numbers in all relevant computations. It is also capable of determining multiple roots and proves to be most efficient when compared to other, similar, existing techniques.
It is maintained that integrated optics will play a major role in the next generation of fiber gyros since the potential exists for mass producing low-cost integrated gyro front-end circuits. Ti:LiNbO3 wave guide technology has been used to demonstrate all the necessary components. The combined use of the 3dB splitter and polarizer functions in a 3 x 3 directional coupler is considered. Such a device was designed for operation at lambda = 1.3 microns and fabricated with 6.5-micron Ti strip widths, and a 1050 C/6 hr diffusion.
Integrated three-waveguide directional coupler functions as polarizer and splitter. Designed with transverse electric (TE) polarization in bar state (two coupling lengths) and transverse magnetic (TM) polarization in cross state (one coupling length). Intended for eventual fabrication as in mass-producible integrated optical circuit that provides advantages including low drive voltage, large-bandwidth phase modulation, preservation of polarization in transmission between devices on same substrate, and low cost.
Current documentation and software do not adequately address the calculation and use of the optimal weight matrices involved in calibrating inertial reference units (IRU). Several facets of the GRO IRU calibration as it relates to the bias and misalignment weighting matrices are investigated. The physical meaning and use of the bias and misalignment weight matrices in IRU calibration are examined. The relation of the weighting and the final biases, misalignments, and their corrections are pursued. Methods for determining reliable, realistic weighting matrices to be used in the GRO IRU calibration (IRUCAL) utility are determined. Possible correlations among observation uncertainties are also explored. For the undetermined case where the maneuvers are insufficient to identify all calibration parameters, the weighting matrices allow as much information as possible to be extracted from the measurements. Finally, applicable simulated flight data are used, incorporating the appropriate calibration maneuvers, to test the weighting matrices in the IRUCAL utility, and examine correlation effects.
Report describes details of implementation of procedure for accurate and economical computation of natural frequencies and associated vibrational modes of elastic structure rotating along arbitrary axis. Block version of Lanczos algorithm derived for solution of eigenvalue and eigenvector problems. Fully exploits sparsity of associated matrices and employs only real numbers in all relevant computations. Capable of determining multiple roots and proves to be most efficient when compared to other similar existing techniques.
Navigation grade fiber optic rotation sensors (FORS) are being developed as an alternative to spinning mass gyro's for unmanned planetary exploration spacecraft. FORS is attractive because of its many advantages such as long life, low weight, low power, and low cost as compared to its mechanical counterparts. FORS incorporates an advanced integrated optics circuit. The advanced eight-component integrated optics circuit performs all the key signal processing functions and in addition incorporates a unique optical beat detection circuit thereby providing an output in the form of pulses proportional to incremental angular position similar to a ring laser gyro (RLG) but without the inherent lock-in problem RLG's possess.
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The dependence of the spin-up system efficiency on each geometrical parameter of the spin-up channel and the exhaust passage of the Gravity Probe-B (GPB) is individually investigated. The spin-up model is coded into a computer program which simulates the spin-up process. Numerical results reveal optimal combinations of the geometrical parameters for the ultimate spin-up performance. Comparisons are also made between the numerical results and experimental data. The experimental leakage rate can only be reached when the gap between the channel lip and the rotor surface increases beyond physical limit. The computed rotating frequency is roughly twice as high as the measured ones although the spin-up torques fairly match.
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A possibility of an effective damping of rotor nutations by modulating the field of the moment transducers in synchronism with the nutation frequency is considered. The algorithms for forming the control moments are proposed and their application is discussed.
This report gives the results of an investigation on the transition from spin about the axis of minimum moment of inertia to spin about the axis of maximum moment of inertia by dissipation of internal mechanical energy. A mathematical discussion, together with charts and diagrams, shows that angular velocities and nutation angle are dependent on the energy and symmetry factors. The low stability of rotation about the axis of maximum moment of inertia, when this inertia is only slightly greater than the mean moment of inertia, is shown.
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In this paper, we present recent work on the design, fabrication, and packaging of a silicon MIcro-Electro-Mechanical System (MEMS) microgyroscope designed for space applications. A hermetically sealed package that houses the microgyroscope and most of its control electronics has been built and tested.
To achieve a drive-axis oscillation with improved frequency and amplitude stability, additional feedback loops are used to adjust force-feedback loop parameters. An amplitude-control loop measures oscillation amplitude, compares this value to the desired level, and adjusts damping of the mechanical sense-element to grow or shrink oscillation amplitude as appropriate. A frequency-tuning loop measures the oscillation frequency, compares this value with a highly stable reference, and adjusts the gain in the force-feedback loop to keep the drive-axis oscillation frequency at the reference value. The combined topology simultaneously controls both amplitude and frequency. Advantages of the combined topology include improved stability, fast oscillation start-up, low power consumption, and excellent shock rejection.