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NASA NTRS2000

Physics of Hard Spheres Experiment: Significant and Quantitative Findings Made

Direct examination of atomic interactions is difficult. One powerful approach to visualizing atomic interactions is to study near-index-matched colloidal dispersions of microscopic plastic spheres, which can be probed by visible light. Such spheres interact through hydrodynamic and Brownian forces, but they feel no direct force before an infinite repulsion at contact. Through the microgravity flight of the Physics of Hard Spheres Experiment (PHaSE), researchers have sought a more complete understanding of the entropically driven disorder-order transition in hard-sphere colloidal dispersions. The experiment was conceived by Professors Paul M. Chaikin and William B. Russel of Princeton University. Microgravity was required because, on Earth, index-matched colloidal dispersions often cannot be density matched, resulting in significant settling over the crystallization period. This settling makes them a poor model of the equilibrium atomic system, where the effect of gravity is truly negligible. For this purpose, a customized light-scattering instrument was designed, built, and flown by the NASA Glenn Research Center at Lewis Field on the space shuttle (shuttle missions STS 83 and STS 94). This instrument performed both static and dynamic light scattering, with sample oscillation for determining rheological properties. Scattered light from a 532- nm laser was recorded either by a 10-bit charge-coupled discharge (CCD) camera from a concentric screen covering angles of 0 to 60 or by sensitive avalanche photodiode detectors, which convert the photons into binary data from which two correlators compute autocorrelation functions. The sample cell was driven by a direct-current servomotor to allow sinusoidal oscillation for the measurement of rheological properties. Significant microgravity research findings include the observation of beautiful dendritic crystals, the crystallization of a "glassy phase" sample in microgravity that did not crystallize for over 1 year in 1g (Earth's gravity), and the emergence of face-centered-cubic (FCC) crystals late in the coarsening process (as small crystallites lost particles to the slow ripening of large crystallites). Significant quantitative findings from the microgravity experiments have been developed describing complex interactions among crystallites during the growth process, as concentration fields overlap in the surrounding disordered phase. Time-resolved Bragg scattering under microgravity captures one effect of these interactions quite conclusively for the sample at a volume fraction of 0.528. From the earliest time until the sample is almost fully crystalline, the size and overall crystallinity grow monotonically, but the number of crystallites per unit volume (number density) falls. Apparently nucleation is slower than the loss of crystallites because of the transfer of particles from small to large crystals. Thus, coarsening occurs simultaneously with growth, rather than following the completion of nucleation and growth as is generally assumed. In the same sample, an interesting signature appears in the apparent number density of crystallites and the volume fraction within the crystallites shortly before full crystallinity is reached. A brief upturn in both indicates the creation of more domains of the size of the average crystallite simultaneous with the compression of the crystallites. Only the emergence of dendritic arms offers a reasonable explanation. The arms would be "seen" by the light scattering as separate domains whose smaller radii of curvature would compress the interior phase. In fiscal year 1999, numerous papers, a doctoral dissertation, and the PHaSE final report were produced. Although this flight project has been completed, plans are in place for a follow-on colloid experiment by Chaikin and Russel that employs a light microscope within Glenn's Fluids and Combustion Facility on the International Space Station. PHaSE is providing us with a deeper understanding of the nure of phase transitions. The knowledge derived has added to the understanding of condensed matter. In addition, the burgeoning study of the dynamics of colloidal self-assembly may lead to the development of a range of photonic materials that control the desirable properties of light. Thus, applications of ordered colloidal structures include not only ultrastructure ceramics, but also photonic crystals and photothermal nanosecond light-switching devices. Industries dealing with semiconductors, electro-optics, ceramics, and composites stand to benefit from such advancements.

Doherty, Michael P.↗

NASA NTRSDate not supplied

Structural Dynamic Analysis in Rocket Propulsion and Launch Vehicles

Structural dynamics is one of the critical disciplines for the successful design, development, and testing of space launch vehicles. It is applied from the smallest component (turbine blades), all the way to the entire vehicle, and has to be calculated for every phase of a mission, from ascent and orbit to landing. Successful application of structural dynamics requires extensive knowledge of Fourier techniques, linear algebra, random variables, finite element modeling, and essentials of SDOF and MDOF vibration theory. Working knowledge of fluid dynamics, statistics, and data analysis also extremely useful.

Andrew M Brown↗

NASA NTRS1987

Statistics and dynamics of persistent anomalies

Persistent anomalies with recurrent spatial patterns play an important role in the atmosphere's low-frequency variability. A connection between statistical and dynamical methods of description and prediction of persistent anomalies is established by computing and analyzing the empirical orthogonal functions (EOFs) in a simple deterministic model, on the one hand, and in Southern Hemisphere geopotential heights, on the other. The dynamical model is governed by the fully nonlinear, equivalent-barotropic vorticity equation on the sphere, with simplified forcing, dissipation and topography. The Southern Hemisphere data consist in gridded daily maps of 500 mb heights from June 1972 to July 1983. Two types of persistent anomalies appear in this time series, both having a strong wavenumber-three component; they differ by the value of the constant phase of this wave and by the strength of the wavenumber-one component. The first two EOFs bear a striking resemblance to these two patterns. It is concluded that the dynamical interpretation of EOFs is their pointing from the time mean to the most populated regions of the system's phase space. Pursuing this interpretation, a Markov-chain formulation of transitions from one persistent anomaly regime to another is introduced, and the implications for long-range forecasting are discussed.

Mo, Kingtse C.↗

NASA NTRS1988

The dynamics and control of large-flexible space structures, part 10

A mathematical model is developed to predict the dynamics of the proposed orbiting Spacecraft Control Laboratory Experiment (SCOLE) during the station keeping phase. The equations of motion are derived using a Newton-Euler formulation. The model includes the effects of gravity, flexibility, and orbital dynamics. The control is assumed to be provided to the system through the Shuttle's three torquers, and through six actuators located by pairs at two points on the mast and at the mass center of the reflector. The modal shape functions are derived using the fourth order beam equation. The generic mode equations are derived to account for the effects of the control forces on the modal shape and frequencies. The equations are linearized about a nominal equilibrium position. The linear regulator theory is used to derive control laws for both the linear model of the rigidized SCOLE as well as that of the actual SCOLE including the first four flexible modes. The control strategy previously derived for the linear model of the rigidized SCOLE is applied to the nonlinear model of the same configuration of the system and preliminary single axis slewing maneuvers conducted. The results obtained confirm the applicability of the intuitive and appealing two-stage control strategy which would slew the SCOLE system, as if rigid to its desired position and then concentrate on damping out the residual flexible motions.

Bainum, Peter M.↗

NASA NTRS1992

The kinematics of buoyancy induced mixing

A model problem to study mixing driven by buoyancy flow fields due to a time dependent body force which consists of a steady and an oscillatory component is considered. Flow fields generated by a time dependent body force, which consists of a steady and an oscillatory component from vibrations or g-jitter, mix two fluids inside a cavity by stretching and folding the interface into various morphological patterns. These patterns show two basic structures depending on the dominant components of the body force. These structures are whirls and tendrils, corresponding to the dominance of either the steady or oscillatory component, respectively. A combination of these structures also occurs in the interaction region. In this region the effect of the steady component opposes the oscillatory component and the result is to smooth the interface, and prevent breakup of the interface. For the parametric range considered, two basic flow regimes occur: convective and chaotic. In the convective regime, the morphological patterns are topological. In the chaotic regime, mixing occurs by a repetitive sequence of bubble formation, necking, and breakup which spreads the concentration field throughout the cavity. The length stretch of the interface increases exponentially with time. The dynamical system characteristics show that in the convective regime, at a point in space, the flow field is oscillatory with elliptical phase space trajectories, and its power spectrum indicates that the flow field responds to the corresponding input frequency. Whereas, in the chaotic regime, the flow field is aperiodic, the phase space trajectories show irregular patterns, and the power spectrum shows a broadband distribution.

Duval, Walter M. B.↗

NASA NTRS1998

A Monte Carlo Uncertainty Analysis of Ozone Trend Predictions in a Two Dimensional Model

We use Monte Carlo analysis to estimate the uncertainty in predictions of total O3 trends between 1979 and 1995 made by the Goddard Space Flight Center (GSFC) two-dimensional (2D) model of stratospheric photochemistry and dynamics. The uncertainty is caused by gas-phase chemical reaction rates, photolysis coefficients, and heterogeneous reaction parameters which are model inputs. The uncertainty represents a lower bound to the total model uncertainty assuming the input parameter uncertainties are characterized correctly. Each of the Monte Carlo runs was initialized in 1970 and integrated for 26 model years through the end of 1995. This was repeated 419 times using input parameter sets generated by Latin Hypercube Sampling. The standard deviation (a) of the Monte Carlo ensemble of total 03 trend predictions is used to quantify the model uncertainty. The 34% difference between the model trend in globally and annually averaged total O3 using nominal inputs and atmospheric trends calculated from Nimbus 7 and Meteor 3 total ozone mapping spectrometer (TOMS) version 7 data is less than the 46% calculated 1 (sigma), model uncertainty, so there is no significant difference between the modeled and observed trends. In the northern hemisphere midlatitude spring the modeled and observed total 03 trends differ by more than 1(sigma) but less than 2(sigma), which we refer to as marginal significance. We perform a multiple linear regression analysis of the runs which suggests that only a few of the model reactions contribute significantly to the variance in the model predictions. The lack of significance in these comparisons suggests that they are of questionable use as guides for continuing model development. Large model/measurement differences which are many multiples of the input parameter uncertainty are seen in the meridional gradients of the trend and the peak-to-peak variations in the trends over an annual cycle. These discrepancies unambiguously indicate model formulation problems and provide a measure of model performance which can be used in attempts to improve such models.

Considine, D. B.↗

NASA NTRS1999

Thermal Radiator Pointing for International Space Station

In order to provide thermal radiation environments that result in adequate beat rejection, the single-phase, liquid ammonia (NH3) heat rejection system on the International Space Station (ISS) requires that its two thermal radiator wings be dynamically rotated as the ISS travels through its orbit. This paper discusses the closed-loop, thermal radiator pointing system that is used on ISS to ensure adequate heat rejection by the radiators, while preventing freezing of the ammonia under low heat loads and cold-environmental conditions. Although initial designs used an open-loop approach for radiator pointing, concerns about performance robustness, algorithm complexity, memory requirements, and sustaining support drove the development of a more robust, simpler, closed-loop system. Hence, the challenge of the closed-loop system was to utilize existing sensors, actuators and computers to fit into the existing hardware and software architecture of the ISS. Using a proportional-integral (PI) control architecture with limited output and an anti-windup integrator, the temperature of the ammonia coming out of the radiator is measured and controlled by adjusting the radiator wing orientation. The radiator wing orientation for the local minimum environment is fed forward to the control system, and the closed-loop controller is used to generate a bias off of that local minimum environment in order to heat up the ammonia when necessary to avoid freezing. In the earth's shadow, the controller is suspended and the radiator wing is oriented to face the earth, the local maximum thermal environment which further prevents freezing of the ammonia. This control architecture is shown to provide adequate heat rejection and avoid freezing of the ammonia, even though the physical system consists of large transport delays and time-varying dynamics which change dramatically due to orbit motion and variable heat loads.

Green, Scott↗

NASA NTRS2006

Granular Contact Forces: Proof of "Self-Ergodicity" by Generalizing Boltzmann's Stosszahlansatz and H Theorem

Ergodicity is proved for granular contact forces. To obtain this proof from first principles, this paper generalizes Boltzmann's stosszahlansatz (molecular chaos) so that it maintains the necessary correlations and symmetries of granular packing ensembles. Then it formally counts granular contact force states and thereby defines the proper analog of Boltzmann's H functional. This functional is used to prove that (essentially) all static granular packings must exist at maximum entropy with respect to their contact forces. Therefore, the propagation of granular contact forces through a packing is a truly ergodic process in the Boltzmannian sense, or better, it is self-ergodic. Self-ergodicity refers to the non-dynamic, internal relationships that exist between the layer-by-layer and column-by-column subspaces contained within the phase space locus of any particular granular packing microstate. The generalized H Theorem also produces a recursion equation that may be solved numerically to obtain the density of single particle states and hence the distribution of granular contact forces corresponding to the condition of self-ergodicity. The predictions of the theory are overwhelmingly validated by comparison to empirical data from discrete element modeling.

Metzger, Philip T.↗

NASA NTRS1989

Explicit modeling and computational load distribution for concurrent processing simulation of the space station

Two important aspects of concurrent processing under development at TRW are discussed. These are: (1) the derivation of explicit mathematical models of multibody dynamic systems, and (2) a balanced computational load distribution (BCLD) among loosely coupled computational units (processors) of a concurrent processing system. The developed methodologies are demonstrated by way of an application to the Phase 1 of the Space Station - a task being performed by TRW under NASA/JSC contract NAS9-17778. The mathematical model of the Space Station consists of three interconnected flexible bodies capable of undergoing large, rigid-body motion with respect to each other. Body 1 is the main central body and contains the pressurized modules inboard of the two Alpha gimbals. Bodies 2 and 3 are the starboard and port bodies connected to Body 1 at the Alpha gimbals and include all components on the transverse booms outboard of the Alpha gimbals (including the solar arrays). The control systems in the model maintain Body 1 in a prescribed 3-axis attitude control mode, while producing large-angle rotations of the flexible solar arrays to position them normal to the sun-line.

Gluck, R.↗

NASA NTRS1989

Efficient sensitivity analysis and optimization of a helicopter rotor

Aeroelastic optimization of a system essentially consists of the determination of the optimum values of design variables which minimize the objective function and satisfy certain aeroelastic and geometric constraints. The process of aeroelastic optimization analysis is illustrated. To carry out aeroelastic optimization effectively, one needs a reliable analysis procedure to determine steady response and stability of a rotor system in forward flight. The rotor dynamic analysis used in the present study developed inhouse at the University of Maryland is based on finite elements in space and time. The analysis consists of two major phases: vehicle trim and rotor steady response (coupled trim analysis), and aeroelastic stability of the blade. For a reduction of helicopter vibration, the optimization process requires the sensitivity derivatives of the objective function and aeroelastic stability constraints. For this, the derivatives of steady response, hub loads and blade stability roots are calculated using a direct analytical approach. An automated optimization procedure is developed by coupling the rotor dynamic analysis, design sensitivity analysis and constrained optimization code CONMIN.

Lim, Joon W.↗

NASA NTRS2020

Design and Test of an Electromechanical Rover Tether for the Exploration of Vertical Lunar Pit

Moon Diver is a proposed mission to land and deploy an extreme-terrain, tethered rover for the exploration of Tranquillitatis Pit, a large vertical cave entrance into the subsurface of Earth’s Moon. By leveraging a supportive tether, the Axel rover, developed by NASA’s Jet Propulsion Laboratory, would perform a controlled descent into the pit and deploy instruments along the pit wall. The purpose of this mission concept is to study a volcanic secondary crust as a function of depth in order to determine formation processes and chemical makeup. The lifeline of the mission would be the tether, which provides power from, and communication to the top-side lander. Critically, the tether also serves as mechanical support between the suspended rover and the lander, which acts as an anchor. While space tethers have been deployed both in orbit and terrestrially, the use of the proposed tether is unlike any known in the literature; the tether must come into contact with the terrain while under load. With respect to the environment, the tether must also survive abrasion from glassy regolith and volcanic rocks, bending around sharp edges, thermal extremes, and exposure to full spectrum ultra-violet (UV) radiation, all while reliably transferring up to 100 W of power and 1 Mbps of data. Furthermore, since the Axel rover pays out tether from an internal spool, the tether’s diameter must be minimized to increase spool capacity, allowing for up to a 300-m traverse while also meeting static and dynamic strength requirements. This paper covers several phases of the tether’s initial development, including i) a trade study of structure and materials with consideration for space heritage, ii) selected design justification, and iii) results from tests on prototype tethers looking into mechanical, electrical, and environmental properties, including exposure to rock regolith abrasion, load profiles at temperature, and degradation due to UV exposure while exposed to vacuum. Finally, we provide insights and lessons learned from lab and field tests, which inform our continued effort to design a tether capable of surviving rugged, lunar conditions.

Nensas, Issa↗

NASA NTRS1993

A review of design concepts for the Advanced Fluids Module (AFM) project

This paper reviews preliminary fluid module design concepts for the Advanced Fluids Module (AFM) project. The objective of this effort is to provide a facility that can handle a wide variety of fluids experiments. Sample science requirements were written and conceptual designs were subsequently generated during the last year. Experiments from the following fluid physics subject areas were used as conceptual design drivers: static and dynamic interfacial phenomena; bubble/droplet thermocapillary migration; surface tension convection and instabilities; thermal/solutal convection; pool boiling; and multiphase flow. After the conceptual designs were completed, the next phase attempted to combine experiments capabilities into a multipurpose, multiuser apparatus configured for the Space Station Freedom. It was found that all the fluid subject areas considered could be accommodated by three basic types of fluids modules. These modules are the Static Fluid Cell Module, the Dynamic Fluid Cell Module, and the Multiphase Flow Module. Descriptions of these preliminary modules designs and their particular sub-systems (e.g., fluid and thermal systems) are discussed. These designs will be refined as the nature of the flight program becomes clearer over the next six to twelve months.

Hill, Myron E.↗

NASA NTRS1987

Product assurance policies and procedures for flight dynamics software development

The product assurance policies and procedures necessary to support flight dynamics software development projects for Goddard Space Flight Center are presented. The quality assurance and configuration management methods and tools for each phase of the software development life cycles are described, from requirements analysis through acceptance testing; maintenance and operation are not addressed.

Perry, Sandra↗

NASA NTRS1993

Kalman filtering applied to real-time monitoring of apogee maneuvers

Part of the Space Mathematics Division in CNES, the Flight Dynamics Center provides attitude and orbit determinations and maneuvers during the Launch and Early Operation Phase (LEOP) of geostationary satellites. Orbit determination is based on a Kalman filter method; when the 2 GHz CNES/NASA network is used, Doppler measurements are available and allow orbit determination during the apogee maneuvers. This method was used for TELE-X and TDF 2 LEOP (3-axis controlled satellites) and also for TELECOM 2 and HISPASAT (spun satellites): it enables us to follow the evolution of the maneuver and gives out a quite accurate estimation of the reached orbit. In this paper, we briefly describe the dynamic models of the orbit evolution in both cases, '3-axis' and 'inertial' thrust. Then, we present the results obtained for each case. Afterwards, we present some cases to show the robustness of the filter.

Deboer, Frederic↗

NASA NTRS2004

Multi-Element Unstructured Analyses of Complex Valve Systems

The safe and reliable operation of high pressure test stands for rocket engine and component testing places an increased emphasis on the performance of control valves and flow metering devices. In this paper, we will present a series of high fidelity computational analyses of systems ranging from cryogenic control valves and pressure regulator systems to cavitating venturis that are used to support rocket engine and component testing at NASA Stennis Space Center. A generalized multi-element framework with sub-models for grid adaption, grid movement and multi-phase flow dynamics has been used to carry out the simulations. Such a framework provides the flexibility of resolving the structural and functional complexities that are typically associated with valve-based high pressure feed systems and have been difficult to deal with traditional CFD methods. Our simulations revealed a rich variety of flow phenomena such as secondary flow patterns, hydrodynamic instabilities, fluctuating vapor pockets etc. In the paper, we will discuss performance losses related to cryogenic control valves, and provide insight into the physics of the dominant multi-phase fluid transport phenomena that are responsible for the choking like behavior in cryogenic control elements. Additionally, we will provide detailed analyses of the modal instability that is observed in the operation of the dome pressure regulator valve. Such instabilities are usually not localized and manifest themselves as a system wide phenomena leading to an undesirable chatter at high flow conditions.

Sulyma, Peter↗

NASA NTRS2014

Data Mining of Historical Human Data to Assess the Risk of Injury due to Dynamic Loads

The NASA Occupant Protection Group is charged with ensuring crewmembers are protected during all dynamic phases of spaceflight. Previous work with outside experts has led to the development of a definition of acceptable risk (DAR) for space capsule vehicles. The DAR defines allowable probability rates for various categories of injuries. An important question is how to validate these probabilities for a given vehicle. One approach is to impact test human volunteers under projected nominal landing loads. The main drawback is the large number of subject tests required to attain a reasonable level of confidence that the injury probability rates would meet those outlined in the DAR. An alternative is to mine existing databases containing human responses to impact. Testing an anthropomorphic test device (ATD) at the same human‐exposure levels could yield a range of ATD responses that would meet DAR. As one aspect of future vehicle validation, the ATD could be tested in the vehicle's seat and suit configuration at nominal landing loads and compared with the ATD responses supported by the human data set. This approach could reduce the number of human‐volunteer tests NASA would need to conduct to validate that a vehicle meets occupant protection standards. METHODS: The U.S. Air Force has recorded hundreds of human responses to frontal, lateral, and spinal impacts at many acceleration levels and pulse durations. All of this data are stored on the Collaborative Biomechanics Data Network (CBDN), which is maintained by the Wright Patterson Air Force Base (WPAFB). The test device for human occupant restraint (THOR) ATD was impact tested on WPAFB's horizontal impulse accelerator (HIA) matching human‐volunteer exposures on the HIA to 5 frontal and 3 spinal loading conditions. No human injuries occurred as a result of these impact conditions. Peak THOR response variables for neck axial tension and compression, and thoracic‐spine axial compression were collected. Maximal chest deflection was determined from motion capture video of the impact test. HIC‐ 15 and BRIC were calculated from head acceleration responses. Given the number of human subjects for each test condition a confidence interval of injury probability will be obtained. RESULTS: Results will be discussed in terms of injury‐risk probability estimates based on the human data set evaluated. Also, gaps in the data set will be identified. These gaps could be one of two types. One is areas where additional THOR testing would increase the comparable human data set, thereby improving confidence in the injury probability rate. The other is where additional human testing would assist in obtaining information on other acceleration levels or directions. DISCUSSION: The historical human data showed validity of the THOR ATD for supplemental testing. The historical human data are limited in scope, however. Further data are needed to characterize the effects of sex, age, anthropometry, and deconditioning due to spaceflight on risk of injury

Wells, Jesica↗

NASA NTRS2016

Analysis of One-Way Laser Ranging Data to LRO, Time Transfer and Clock Characterization

We processed and analyzed one-way laser ranging data from International Laser Ranging Service ground stations to NASA's Lunar Reconnaissance Orbiter (LRO), obtained from June 13, 2009 until September 30, 2014. We pair and analyze the one-way range observables from station laser fire and spacecraft laser arrival times by using nominal LRO orbit models based on the GRAIL gravity field. We apply corrections for instrument range walk, as well as for atmospheric and relativistic effects. In total we derived a tracking data volume of approximately 3000 hours featuring 64 million Full Rate and 1.5 million Normal Point observations. From a statistical analysis of the dataset we evaluate the experiment and the ground station performance. We observe a laser ranging measurement precision of 12.3 centimeters in case of the Full Rate data which surpasses the LOLA (Lunar Orbiting Laser Altimeter) timestamp precision of 15 centimeters. The averaging to Normal Point data further reduces the measurement precision to 5.6 centimeters. We characterized the LRO clock with fits throughout the mission time and estimated the rate to 6.9 times10 (sup -8), the aging to 1.6 times 10 (sup -12) per day and the change of aging to 2.3 times 10 (sup -14) per day squared over all mission phases. The fits also provide referencing of onboard time to the TDB (Barycentric Dynamical Time) time scale at a precision of 166 nanoseconds over two and 256 nanoseconds over all mission phases, representing ground to space time transfer. Furthermore we measure ground station clock differences from the fits as well as from simultaneous passes which we use for ground to ground time transfer from common view observations. We observed relative offsets ranging from 33 to 560 nanoseconds and relative rates ranging from 2 times 10 (sup -13) to 6 times 10 (sup -12) between the ground station clocks during selected mission phases. We study the results from the different methods and discuss their applicability for time transfer.

Bauer, S.↗

NASA NTRS2013

Optimal Recursive Digital Filters for Active Bending Stabilization

In the design of flight control systems for large flexible boosters, it is common practice to utilize active feedback control of the first lateral structural bending mode so as to suppress transients and reduce gust loading. Typically, active stabilization or phase stabilization is achieved by carefully shaping the loop transfer function in the frequency domain via the use of compensating filters combined with the frequency response characteristics of the nozzle/actuator system. In this paper we present a new approach for parameterizing and determining optimal low-order recursive linear digital filters so as to satisfy phase shaping constraints for bending and sloshing dynamics while simultaneously maximizing attenuation in other frequency bands of interest, e.g. near higher frequency parasitic structural modes. By parameterizing the filter directly in the z-plane with certain restrictions, the search space of candidate filter designs that satisfy the constraints is restricted to stable, minimum phase recursive low-pass filters with well-conditioned coefficients. Combined with optimal output feedback blending from multiple rate gyros, the present approach enables rapid and robust parametrization of autopilot bending filters to attain flight control performance objectives. Numerical results are presented that illustrate the application of the present technique to the development of rate gyro filters for an exploration-class multi-engined space launch vehicle.

Orr, Jeb S.↗