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All sourcesNASA NTRSDOE OSTI
NASA NTRS2004

Two-Armed, Mobile, Sensate Research Robot

The Anthropomorphic Robotic Testbed (ART) is an experimental prototype of a partly anthropomorphic, humanoid-size, mobile robot. The basic ART design concept provides for a combination of two-armed coordination, tactility, stereoscopic vision, mobility with navigation and avoidance of obstacles, and natural-language communication, so that the ART could emulate humans in many activities. The ART could be developed into a variety of highly capable robotic assistants for general or specific applications. There is especially great potential for the development of ART-based robots as substitutes for live-in health-care aides for home-bound persons who are aged, infirm, or physically handicapped; these robots could greatly reduce the cost of home health care and extend the term of independent living. The ART is a fully autonomous and untethered system. It includes a mobile base on which is mounted an extensible torso topped by a head, shoulders, and two arms. All subsystems of the ART are powered by a rechargeable, removable battery pack. The mobile base is a differentially- driven, nonholonomic vehicle capable of a speed >1 m/s and can handle a payload >100 kg. The base can be controlled manually, in forward/backward and/or simultaneous rotational motion, by use of a joystick. Alternatively, the motion of the base can be controlled autonomously by an onboard navigational computer. By retraction or extension of the torso, the head height of the ART can be adjusted from 5 ft (1.5 m) to 6 1/2 ft (2 m), so that the arms can reach either the floor or high shelves, or some ceilings. The arms are symmetrical. Each arm (including the wrist) has a total of six rotary axes like those of the human shoulder, elbow, and wrist joints. The arms are actuated by electric motors in combination with brakes and gas-spring assists on the shoulder and elbow joints. The arms are operated under closed-loop digital control. A receptacle for an end effector is mounted on the tip of the wrist and contains a force-and-torque sensor that provides feedback for force (compliance) control of the arm. The end effector could be a tool or a robot hand, depending on the application.

Engelberger, J. F.↗
NASA NTRS1992

The dimension of attractors underlying periodic turbulent Poiseuille flow

A lower bound on the Liapunov dimenison, D-lambda, of the attractor underlying turbulent, periodic Poiseuille flow at a pressure-gradient Reynolds number of 3200 is calculated, on the basis of a coarse-grained (16x33x8) numerical solution, to be approximately 352. Comparison of Liapunov exponent spectra from this and a higher-resolution (16x33x16) simulation on the same spatial domain shows these spectra to have a universal shape when properly scaled. On the basis of these scaling properties, and a partial exponent spectrum from a still higher-resolution (32x33x32) simulation, it is argued that the actual dimension of the attractor underlying motion of the given computational domain is approximately 780. It is suggested that this periodic turbulent shear flow is deterministic chaos, and that a strange attractor does underly solutions to the Navier-Stokes equations in such flows.

Keefe, Laurence↗
NASA NTRS1995

Speed Discrimination: Multiple Stimuli Appear Better Than One

We reported that for a 21FC task with multiple moving grating patches (Gabors) in each interval, thresholds for speed discrimination decreased with the number of patches, while increasing the area of a single grating produced no such effect. Furthermore, this decrease occurred regardless of the spacing of the patches about a circle of eccentricity 4 degrees, i.e., whether they were maximally separated or almost touching. These results suggest that it is the multiple, discrete grating patches that cause thresholds to decrease, rather than the spatial arrangement. To test this hypothesis, we measured the effect of dividing a large grating into four quadrants, by superimposing a mean-luminance cross on it. The mean speed discrimination thresholds (Weber Fractions) for four observers were 19, 15, and 11 plus or minus 2%, for the single large grating, the grating with cross, and the 4 maximally-separated, small gratings, respectively. Thus, breaking up a single large grating into multiple parts caused thresholds to improve, despite the fact that less of the original patch was visible. To investigate the possible contribution of total bounding contour length, we measured the effect of coalescing three small grating patches into a single banana-shaped patch, while keeping the total contour length constant. These two conditions were compared to a single, circular Gabor patch of equivalent area that had (necessarily) a smaller contour length. Preliminary data from 3 of 4 observers were similar for the small-grating and banana configurations, but increased for the single, large grating, suggesting that contour length might play a role. We are also investigating the role of low-level factors pertinent to the large grating, such as the pooling of signals from motion units at different eccentricities, and the stimulation of extended inhibitory motion surrounds, as well as the possible contribution of topdown influences that segment the stimulus into distinct objects.

Verghese, Preeti↗
NASA NTRS1991

Limits on the isolation of stochastic vibration for microgravity space experiments

The limitations on the isolation of stochastic vibrations for microgravity space experiments are explored. These limitations result from the restricted interior space available for vibration isolation. A one-degree-of-freedom representation of the experiment-spacecraft system is used, and an ideal vibration actuator is assumed. A kinematic representation results, and the problem becomes one of finding the minimum acceleration trajectory within a pair of stochastic walls. The wall motion is characterized by an ergodic, stationary, zero-mean, Gaussian random process with known power spectral density. The geometry of the wall trajectories is defined in terms of their significant extrema and zero crossings. This geomemtry is used in defining a composite trajectory that has a mean square acceleratiaon lower than that on the optimal path satisfying the stochastic wall inequality constraints. The optimal control problem is solved on a return path yielding the mean square acceleration in terms of the distributions of significant maxima and first-passage time of the wall process. The methodology is applied to a microgravity isolation problem to find the lower bounds on root-mean-square acceleration given the disturbance power spectral density.

Knospe, C. R.↗
NASA NTRS1993

Orbital simulations of satellite escape/capture and the origin of satellites such as Triton

We investigate satellite escape/capture in the context of the restricted, circular three body problem as applied to the Sun, Neptune, and Triton. We have computed a large number of coplanar prograde and retrograde orbital simulations over a range of initial distances and velocities. The satellite starts at superior conjunction within approximately 2 Hill radii of Neptune and has a velocity orthogonal to the Sun-planet line. Orbits with these initial conditions can be reflected with respect to time, so an escape is simply the reverse of a capture. We numerically integrate the equations of motion to compute the satellite's position until it escapes, collides with Neptune, or after 100 planetary years fails to escape, when computations cease. The initial distance x and velocity v in the restricted problem uniquely define the Jacobi constant C, a conserved energy-like quantity. Plots of the simulation outcomes in the prograde and retrograde C, x phase spaces reveal distinct zones in which temporary satellites approach the planet closely enough that permanent capture can be effected by gas drag with a protoplanetary nebula or by collision with a pre-existing satellite. Single and double close-flybys constitute the most common possible capture orbits. Long term multiple flyby orbits occur near the stability limits between bound and unbound orbits, and are more common among retrograde captures.

Benner, Lance A. M.↗
NASA NTRS1987

Latitudinal motions of the aurora during substorms

Sequences of auroral images obtained with Dynamics Explorer 1 are used to investigate latitudinal motions of the aurora in substorms. Average speeds of poleward motion are about 230 m/s near local midnight for two isolated, small substorms and about 1000 m/s during an intensification within a previously active auroral oval. The speed of poleward expansion measured at about 6-min temporal resolution can differ greatly from the average speed because of the episodic development of substorms. Recovery of the high-latitude boundary of the aurora to presubstorm latitudes is first observed in the postmidnight sector. In the premidnight sector the discrete aurora can become stationary for a period of time or even continue further poleward before a retreat to lower latitudes begins. During the recovery phase, a prominent decrease in luminosities is first observed at intermediate latitudes within the auroral distribution. This region is bounded at higher latitudes by the discrete aurora and at lower latitudes by bright diffuse aurora. Given that magnetic field lines threading these auroral distributions map to the plasma sheet boundary layer and to the central plasma sheet, respectively, magnetic field lines at the intermediate auroral latitudes then map to the plasma sheet at distances of more than about 22 earth radii.

Craven, J. D.↗
NASA NTRS1989

The dynamics and control of large flexible space structures - 12, supplement 11

The rapid 2-D slewing and vibrational control of the unsymmetrical flexible SCOLE (Spacecraft Control Laboratory Experiment) with multi-bounded controls is considered. Pontryagin's Maximum Principle is applied to the nonlinear equations of the system to derive the necessary conditions for the optimal control. The resulting two point boundary value problem is then solved by using the quasilinearization technique, and the near minimum time is obtained by sequentially shortening the slewing time until the controls are near the bang-bang type. The tradeoff between the minimum time and the minimum flexible amplitude requirements is discussed. The numerical results show that the responses of the nonlinear system are significantly different from those of the linearized system for rapid slewing. The SCOLE station-keeping closed loop dynamics are re-examined by employing a slightly different method for developing the equations of motion in which higher order terms in the expressions for the mast modal shape functions are now included. A preliminary study on the effect of actuator mass on the closed loop dynamics of large space systems is conducted. A numerical example based on a coupled two-mass two-spring system illustrates the effect of changes caused in the mass and stiffness matrices on the closed loop system eigenvalues. In certain cases the need for redesigning control laws previously synthesized, but not accounting for actuator masses, is indicated.

Bainum, Peter M.↗
NASA NTRS1985

The polar caps

According to the most common definition, the 'polar cap' is the region bounded by the average or statistical auroral oval. Studies of the effects of the interplanetary magnetic field (IMF) on various upper atmospheric phenomena are reviewed. The Antarctic region and the Arctic region represent an area for such investigations. Particular attention is given in this paper to those observations in the highest latitude region which provide some information concerning corresponding changes of the internal structure of the magnetosphere. A definition and working definition of the polar cap are considered along with the IMF and magnetospheric models, the entry of solar energetic electrons, statistical studies regarding the aurora, individual events, polar cap arcs, the cusp aurora, auroral electron precipitation, convection, ionospheric currents and field-aligned currents, the ionosphere, the thermosphere, polar rain, polar wind, and hopping motions of heavy ions.

Akasofu, S.-I.↗
NASA NTRS2018

NICER Discovers the Ultracompact Orbit of the Accreting Millisecond Pulsar IGR J17062-6143

We present results of recent Neutron Star Interior Composition Explorer (NICER) observations of the accreting millisecond X-ray pulsar (AMXP) IGR J17062-6143 that show that it resides in a circular, ultracompact binary with a 38-minute orbital period. NICER observed the source for 26 kiloseconds over a 5.3-day span in 2017 August, and again for 14 and 11 kiloseconds in 2017 October and November, respectively. A power spectral analysis of the August exposure confirms the previous detection of pulsations at 163.656 Hertz in Rossi X-ray Timing Explorer (RXTE) data, and reveals phase modulation due to orbital motion of the neutron star. A coherent search for the orbital solution using the Z squared method finds a best-fitting circular orbit with a period of 2278.21 seconds (37.97 minutes), a projected semimajor axis of 0.00390 lt-s (Localization Test Statistic), and a barycentric pulsar frequency of 163.6561105 Hertz. This is currently the shortest known orbital period for an AMXP. The mass function is 9.12 times 10 (sup minus 8) solar mass, presently the smallest known for a stellar binary. The minimum donor mass ranges from approximately 0.005 to 0.007 times the solar mass for a neutron star mass from 1.2 to 2 times the solar mass. Assuming mass transfer is driven by gravitational radiation, we find donor mass and binary inclination bounds of 0.0175-0.0155 times the solar mass and 19 degrees less than i less than 27.5 degrees, where the lower and upper bounds correspond to 1.4 and 2 times the solar mass neutron stars, respectively. Folding the data accounting for the orbital modulation reveals a sinusoidal profile with fractional amplitude 2.04 plus or minus 0.11 percent (0.3-3.2 kiloelectronvolts).

Strohmayer, T. E.↗
NASA NTRS1994

Cold, warm, and hot gas in the late-stage merger NGC 7252

We present the first observations of the neutral hydrogen distribution and x-ray emission in the prototypical merger remnant NGC 7252, the 'Atoms-for-Peace' galaxy. These data are supplemented by accurate B and R surface photometry, reaching a limit of mu(sub B) = 26.5 mag/sq arcsec, and images taken through a narrow-band H alpha filter. We find all of the 2 x 10(exp 9)/sq h solar mass of atomic gas to be restricted to the outer, tidal regions of this system (H(sub zero) = 100 h km/s/Mpc). By contrast, the molecular gas traced by the (12)CO(1 approaches zero) map of Wang et al. (1992) is confined to an inner rotating disk of radius 7 seconds and has an H alpha counterpart. The gap between the atomic and molecular gas distributions is filled in by diffuse H alpha emission and perhaps by x-ray emission. The velocity field of the atomic gas in the tidal tails indicates that they are swinging through space in the same sense as the rotation of the inner gas disk. The H I at the apparent base of the northwestern tail seems to be falling back toward the main body of the galaxy, yet there is no H I associated with this main stellar body: This suggests ongoing efficient conversion of the atomic gas into other phases in this region. The H alpha velocity anomalies previously found in the remnant body may be produced in part by the combination of tail-related, noncircular motions and the inner gas-disk rotation. Both tidal tails have bluer B-R colors than the main body of the remnant, with the bluest regions coinciding with peaks in the gas column density. Each tail contains one giant H II region near the end of its optical light distribution. These H II regions are associated with large concentrations of gas and stars that approach the sizes and gas contents of dwarf galaxies. The H I extends beyond the end of the optical tails and reaches projected distances of 62/h kpc east and 120/h kpc northwest from the center. We discuss the possible relevance of these data to : (1) the transformation of merged spirals into ellipticls; (2) the generation of ripples by returning tidal material; and (3) the formation of bound stellar systems from tidally torn material.

Hibbard, J. E.↗
NASA NTRS2010

Shallow and Deep Latent Heating Modes Over Tropical Oceans Observed with TRMM PR Spectral Latent Heating Data

The global hydrological cycle is central to the Earth's climate system, with rainfall and the physics of its formation acting as the key links in the cycle. Two-thirds of global rainfall occurs in the Tropics. Associated with this rainfall is a vast amount of heat, which is known as latent heat. It arises mainly due to the phase change of water vapor condensing into liquid droplets; three-fourths of the total heat energy available to the Earth's atmosphere comes from tropical rainfall. In addition, fresh water provided by tropical rainfall and its variability exerts a large impact upon the structure and motions of the upper ocean layer. Three-dimensional distributions of latent heating estimated from Tropical Rainfall Measuring Mission Precipitation Radar (TRMM PR)utilizing the Spectral Latent Heating (SLH) algorithm are analyzed. Mass-weighted and vertically integrated latent heating averaged over the tropical oceans is estimated as approx.72.6 J/s (approx.2.51 mm/day), and that over tropical land is approx.73.7 J/s (approx.2.55 mm/day), for 30degN-30degS. It is shown that non-drizzle precipitation over tropical and subtropical oceans consists of two dominant modes of rainfall systems, deep systems and congestus. A rough estimate of shallow mode contribution against the total heating is about 46.7 % for the average tropical oceans, which is substantially larger than 23.7 % over tropical land. While cumulus congestus heating linearly correlates with the SST, deep mode is dynamically bounded by large-scale subsidence. It is notable that substantial amount of rain, as large as 2.38 mm day-1 in average, is brought from congestus clouds under the large-scale subsiding circulation. It is also notable that even in the region with SST warmer than 28 oC, large-scale subsidence effectively suppresses the deep convection, remaining the heating by congestus clouds. Our results support that the entrainment of mid-to-lower-tropospheric dry air, which accompanies the large-scale subsidence is the major factor suppressing the deep convection. Therefore, representation of the realistic entrainment is very important for proper reproduction of precipitation distribution and resultant large-scale circulation.

Takayabu, Yukari N.↗
NASA NTRS2022

A Comparative Evaluation of Snowflake Particle Shape Estimation Techniques Used By the Precipitation Imaging Package (PIP), Multi-Angle Snowflake Camera (MASC), and Two-Dimensional Video Disdrometer (2DVD)

Measurements of snowflake particle shape are important for studying snow microphysics. While a number of instruments exist that are capable of measuring particle shape, this study focuses on the measurement techniques of three digital video disdrometers: the Precipitation Imaging Package (PIP), the Multi-Angle Snowflake Camera (MASC), and the Two-Dimensional Video Disdrometer (2DVD). To gain a better understanding of the relative strengths and weaknesses of these instruments and to provide a foundation upon which comparisons can be made between studies using data from different instruments, we perform a comparative analysis of the shape measurement algorithms employed by each of the three instruments by applying the algorithms to snowflake images captured by PIP during the ICE-POP 2018 field campaign. Our analysis primarily focuses on the measurement of the aspect ratio of either the particle itself, in the case of PIP and MASC, or of the particle bounding box, in the case of PIP and 2DVD. Both PIP and MASC use shape-fitting algorithms to measure aspect ratio. While our analysis of the MASC aspect ratio suggests that the measurements are reliable, our findings indicate that both the ellipse and rectangle aspect ratios produced by PIP underperformed considerably due to the shortcomings of the PIP shape-fitting techniques. We also demonstrate that reliable measurements of aspect ratio can be retrieved from PIP by reprocessing the raw PIP images using either the MASC ellipse-fitting algorithm or a tensor-based ellipse-fitting algorithm. Because of differences in instrument design, 2DVD produces measurements of particle horizontal and vertical extent rather than length and width. Furthermore, the 2DVD measurements of particle horizontal extent can be contaminated by horizontal particle motion. Our findings indicate that, although the correction technique used to remove the horizontal motion contamination performs remarkably well with snowflakes despite being designed for use with raindrops, the 2DVD measurements of particle horizontal extent are less reliable than those measured by PIP.

Charles N Helms↗
NASA NTRS1992

Error Analysis of Combined Optical-Flow and Stereo Passive Ranging

The motion of an imaging sensor causes each imaged point of the seem to describe a time trajectory on the image plane. The trajectories of all imaged points are reminiscent of a flow (eg, of liquid) which is the source of the term "optical flow". Optical-flow ranging is a method by which the stream of two-dimensional images obtained from a forward-looking forward-moving passive sensor is used to compute range to points in the field of view. Another well-known ranging method consists of triangulation based on stereo images obtained from at least two stationary sensors. In this paper we analyze the potential accuracies of a combined optical flow and stereo passive-ranging system in the context of helicopter nap-of-the-earth obstacle avoidance. The Cramer-Rao lower bound (CRLB) is developed for the combined system under the assumption of a random angular misalignment common to both cameras of a stereo pair. It is shown that the range accuracy degradations caused by misalignment is negligible for a combined optical-flow and stereo system as compared with a monocular optical-flow system.

Barniv, Yair↗
NASA NTRSDate not supplied

Isolator Shock Train Response to Dual-Mode Scramjet Throttling-Like Forcing

Typical dual-mode scramjet designs employ an isolator component situated between the inlet and combustor. The isolator fluidically buffers the inlet from the combustor via the formation of a shock train, an interconnected series of shock-boundary layer interactions. The isolator is required during ramjet-engine operation and at the lower edges of the scramjet operational envelope. In an operational engine, transient behavior imposes fluidic dynamics due to attitude adjustments, combustor throttling, aberrant resonances within the combustor, etc. To accommodate these transients, the shock train adjusts on both temporal and spatial scales. Sufficiently large downstream pressure increases in the combustor play a critical role during unstart, whereby strong compression waves propagate upstream in the isolator to ultimately force the shock train out the inlet, if it cannot stabilize to the pressure increase. This critically reduces the engine mass flow rate, potentially causing a catastrophic reduction in thrust and loss of the vehicle. A nearly instantaneous unstart can, in principle, be predicted by a ratio of the normal shock pressure jump in an inviscid isolator. However, lower-magnitude perturbations, below this bound, also induce unstarts. Understanding the transient behavior inherent in unsteady isolator operation is critical to reducing safety margin in isolator length and refining engine control algorithms to improve engine performance. The Isolator Dynamics Research Lab (IDRL) is a cold-flow, direct-connect isolator facility ideal for assessing the fundamental fluid dynamics of shock trains. The internal flow of a scramjet isolator is modeled using a 2D, symmetric Mach 2.5 nozzle followed by a 695 mm long, 25.4x50.8 mm rectangular isolator test section. A blockage cone on a high-speed ball screw actuator downstream of the isolator is pulsed to simulate the throttling behavior in an operational combustor. Wall flush high-speed static pressure transducers detect the streamwise shock train within the isolator. Time delays between the onset of the throttling and the response motion of the shock train are analyzed to assess the controlling scales and parameters. From this analysis, the response time of the isolator shock train system is found to depend primarily on the isolator back pressure time-rate-of-change but quickly saturates to a maximum propagation speed along the isolator. These results inform dual-mode scramjet engine designers of the critical parameters and limits of an unstart resistant engine.

scramjet↗
NASA NTRS2000

A Dynamical Model for The Jupiter Thermocline

A new conceptual model for the observed banded wind structure of the giant outer planets is proposed, assuming a smoothly distributed potential vorticity (PV) atop a layer of deeply seated, latitudinally variable stratification. With a vanishing horizontal entropy contrast presumably enforced at the bottom of the flow layer by the underlying convection, the thermal-wind balance of observed cloud-top motions implies a mapping of constant potential temperature surfaces, nearly vertical at upper tropospheric levels, down to a deeper, flatter, but variably sloped 'thermocline.' For a generally colder-poleward distribution of isentropes consistent with the strong equatorial jets of both Jupiter and Saturn, this kind of mapping would also imply a poleward decreasing static stability. The proposed temperature-stability distribution is just the reverse of the Earth's troposphere, where the strongest latitudinal potential temperature gradients are at the bottom instead of the top, with static stability generally increasing toward the pole. The warmer-stabler correlation for Jupiter would be consistent, however, with a nearly monotonic distribution of PV from low to high latitudes, over planetary scales for which the planetary vorticity dominates the relative vorticity of the jets. In this way efficient PV mixing for the isentropically bounded thermocline can account for the dynamical maintenance of the cyclonic flanks of the equatorial jet. Over latitudinal intervals comparable to the internal deformation scale, however, the gradient of the absolute vorticity is dominated by the flow curvature, with the local latitudinal gradient of the static stability proportional to the local potential temperature gradient and therefore the local variation in geostrophic velocity. The resulting correlation of velocities and vorticity gradients implies an alternation of the flow over the internal deformation radius set by the vertical entropy contrast.

Allison, Michael↗
NASA NTRS1991

Error analysis of combined stereo/optical-flow passive ranging

The motion of an imaging sensor causes each imaged point of the scene to correspondingly describe a time trajectory on the image plane. The trajectories of all imaged points are reminiscent of a flow (e.g., of liquid) which is the source of the term 'optical flow'. Optical-flow ranging is a method by which the stream of two-dimensional images obtained from a forward-looking forward-moving passive sensor is used to compute depth (or range) to points in the field of view. Another well-known ranging method consists of triangulation based on stereo images obtained from at least two stationary sensors. In this paper we analyze the potential accuracies of a combined optical flow and stereo passive-ranging system in the context of helicopter nap-of-the-earth obstacle avoidance. The Cramer-Rao lower bound is developed for the combined system under the assumption of an unknown angular bias error common to both cameras of a stereo pair. It is shown that the depth accuracy degradations caused by a bias error is negligible for a combined optical-flow and stereo system as compared to a monocular optical-flow system.

Barniv, Yair↗
NASA NTRS2011

Lateral-Directional Parameter Estimation on the X-48B Aircraft Using an Abstracted, Multi-Objective Effector Model

The problem of parameter estimation on hybrid-wing-body aircraft is complicated by the fact that many design candidates for such aircraft involve a large number of aerodynamic control effectors that act in coplanar motion. This adds to the complexity already present in the parameter estimation problem for any aircraft with a closed-loop control system. Decorrelation of flight and simulation data must be performed in order to ascertain individual surface derivatives with any sort of mathematical confidence. Non-standard control surface configurations, such as clamshell surfaces and drag-rudder modes, further complicate the modeling task. In this paper, time-decorrelation techniques are applied to a model structure selected through stepwise regression for simulated and flight-generated lateral-directional parameter estimation data. A virtual effector model that uses mathematical abstractions to describe the multi-axis effects of clamshell surfaces is developed and applied. Comparisons are made between time history reconstructions and observed data in order to assess the accuracy of the regression model. The Cram r-Rao lower bounds of the estimated parameters are used to assess the uncertainty of the regression model relative to alternative models. Stepwise regression was found to be a useful technique for lateral-directional model design for hybrid-wing-body aircraft, as suggested by available flight data. Based on the results of this study, linear regression parameter estimation methods using abstracted effectors are expected to perform well for hybrid-wing-body aircraft properly equipped for the task.

Ratnayake, Nalin A.↗
NASA NTRS1993

Torque equilibrium attitudes for the Space Station

All spacecraft orbiting in a low earth orbit (LEO) experience external torques due to environmental effects. Examples of these torques include those induced by aerodynamic, gravity-gradient, and solar forces. It is the gravity-gradient and aerodynamic torques that produce the greatest disturbances to the attitude of a spacecraft in LEO, and large asymmetric spacecraft, such as the space station, are affected to a greater degree because the magnitude of the torques will, in general, be larger in proportion to the moments of inertia. If left unchecked, these torques would cause the attitude of the space station to oscillate in a complex manner and the resulting motion would destroy the micro-gravity environment as well as prohibit the orbiter from docking. The application of control torques will maintain the proper attitude, but the controllers have limited momentum capacity. When any controller reaches its limit, propellant must then be used while the device is reset to a zero or negatively-biased momentum state. Consequently, the rate at which momentum is accumulated is a significant factor in the amount of propellant used and the frequency of resupply necessary to operate the station. A torque profile in which the area curve for a positive torque is not equal to the area under the curve for a negative torque is 'biased,' and the consequent momentum build-up about that axis is defined as secular momentum because it continues to grow with time. Conversely, when the areas are equal, the momentum is cyclic and bounded. A Torque Equilibrium Attitude (TEA) is thus defined as an attitude at which the external torques 'balance' each other as much as possible, and which will result in lower momentum growth in the controllers. Ideally, the positive and negative external moments experienced by a spacecraft at the TEA would exactly cancel each other out and small cyclic control torques would be required only for precise attitude control. Over time, the only momentum build-up in the controllers would be due to electro-mechanical losses within the device. However, the atmospheric torques are proportional to the density of the atmosphere and the density varies with the orbital position, time of day, time of year, and the solar cycle. In addition, there are unmodeled disturbances and uncertainties in the mass and inertias. Therefore, there is no constant attitude that will completely balance the environmental torques and the dynamic TEA cannot be solved in closed form. The objective of this research was to determine a method to calculate a dynamic TEA such that the rate of momentum build-up in the controllers would be minimized and to implement this method in the MATRIX(x) simulation software by Integrated Systems, Inc.

Thompson, Roger C.↗