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At least 127 records · Page 7

Trajectories in Close Proximity to Asteroids

Spacecraft motion in close proximity to irregularly shaped, rotating bodies such as asteroids presents a unique dynamical environment as compared to most space missions. There are several fundamental novelties in this environment that spacecraft must deal with. These include the possibility of orbital instabilities that can act over very short time spans (on the order of hours for some systems), possible non-uniform rotation of the central gravity field, divergence of traditional gravity field representations when close to the asteroid surface, dominance of perturbing forces, an extremely large asteroid model parameter space that must be prepared for in the absence of reliable information, and the possibility of employing new and novel trajectory control techniques such as hovering and repeated landings on the asteroid surface. An overview of how these novelties impact the space of feasible close proximity operations and how different asteroid model properties will affect their implementation is given. In so doing, four fundamental types of close proximity operations will be defined. Listed in order of increasing technical difficulty these are: (1) close, stable orbits; (2) low-altitude flyovers; (3) landing trajectories; and (4) hovering trajectories. The feasibility and difficulty of implementing these operations will vary as a function of the asteroid shape, size, density, and rotation properties, and as a function of the spacecraft navigation capability. Additional information is contained in the original extended abstract.

Scheeres, D. J.

Effect of Passive Horizontal Rotations and Vertical Oscillations on Dynamic Visual Acuity

Astronauts experience sensorimotor disturbances after long duration space flight. These crewmembers may need to egress the vehicle within a few minutes for safety and operational reasons in various sea state conditions following a water landing. Exposure to even low frequency motions induced by sea conditions surrounding a vessel can cause significant fine and gross motor control problems affecting critical functions. The objective of this study was to document human motor and visual performance during simulated wave motion in the 0.1 to 2.0 Hz range. We examined in 12 healthy subjects the changes in accuracy when performing a seated visual target acquisition task in which the location of target was offset vertically during horizontal full body rotation at an oscillating frequency of 0.8 Hz (peak velocity of 160 deg/s). The main finding was that the accuracy of performance degraded in 7 of 12 subjects when acquiring vertical targets at perturbing frequencies of 0.8 Hz in the horizontal plane by one step size. We also examined in a separate study on 12 healthy subjects seated dynamic visual acuity (DVA) task performance during vertical full body oscillations at perturbing frequencies of 2 Hz (peak to peak motion of 5 cm). The main finding was that DVA was significantly reduced when acquiring targets at perturbing oscillations at frequencies of 2 Hz in the vertical plane by approximately 1 chart line. Thus low frequencies of perturbations in the horizontal and vertical planes can cause decrement in visual performance.

Mulavara, Ajitkumar

Ionized Gas Kinematics at High Resolution. IV. Star Formation and a Rotating Core in the Medusa (NGC 4194)

NGC 4194 is a post-merger starburst known as The Medusa for its striking tidal features.We present here a detailed study of the structure and kinematics of ionized gas in the central 0.65 kpc of the Medusa. The data include radio continuum maps with resolution up to 0".18 (35 pc) and a 12.8 micron [Ne II] data cube with spectral resolution approx. 4 km/s: the first high-resolution, extinction-free observations of this remarkable object. The ionized gas has the kinematic signature of a core in solid-body rotation. The starburst has formed a complex of bright compact H II regions, probably excited by deeply embedded super star clusters, but none of these sources is a convincing candidate for a Galactic nucleus. The nuclei of the merger partners that created the Medusa have not yet been identified.

Ionized

Detection of a 'rotating' gas cloud 100 kiloparsecs in diameter surrounding 3C 275.1, a quasar at the center of a rich cluster of galaxies

The distorted radio quasar 3C 275.1 (z = 0.55) is the first QSO found to lie at the center of a rich cluster of galaxies. The quasar is surrounded by an extremely large elliptical nebulosity whose major axis exceeds 100 kpc. Spectroscopic observations of this nebulosity were obtained, with the spectrograph slit aligned along the nebulosity's major axis. The spectrum of the nebulosity in the visible is dominated by O II and O III forbidden emission lines, which yield a well-defined 'solid-body rotation curve' extending 40 kpc from the quasar nucleus, a rotation curve very different from those of normal spiral galaxies. The 3C 275.1 nebulosity is both the largest yet discovered around a quasar and the first in which organized large-scale motions (rotation?) have been identified. The nebulosity may be residue from multiple tidal interactions with cluster members, or it may be accumulated material from a 'cooling flow' of the type seen in low-redshift clusters which are X-ray sources.

Hintzen, P.

Ground based studies of the vibrational and rotational dynamics of acoustically levitated drops and shells

A substantial amount of experimental data can be gathered on the dynamics of acoustically positioned liquids in a ground-based laboratory and during short duration low-gravity parabolic flights of the KC-135. The preliminary results of a set of measurements of the static shape, of the vibrational spectrum, and the rotation equilibrium shapes of simple drops and liquid shells carried out using ultrasonic levitators working between 19 and 40 kHz is presented. The droplet diameter ranges between 1 and 5 mm, the surface tension of the liquid used varies between 25 and 70 dynes/cm, and the viscosity is changed between 1 to 1,000 cP. Of particular interest is the variation of the frequency of the fundamental mode of shape oscillation with various factors, and the effects of static drop shape deformation on the limit of stability of the axisymmetric shape of a drop in solid-body rotation.

Trinh, E. H.

Attitude control system synthesis for the Hoop/Column antenna using the LQG/LTR method

This paper investigates the application of the linear-quadratic-Gaussian (LQG)/loop transfer recovery (LTR) method to the problem of synthesizing a fine-pointing control system for a large flexible space anenna. The study is based on an antenna, which consists of three rigid-body rotational modes and the first ten elastic modes. A robust compensator design for achieving the required pointing performance in the presence of modeling uncertainties is obtained using the LQG/LTR method. For the Hoop/Column antenna, a satisfactory controller design meeting a desired bandwidth of .1 rad/sec and ensuring stability with unmodelled high frequency modes is obtained using only a collocated pair of 3-axis attitude sensors and torque actuators. This study also indicates that to achieve the desired performance bandwidth of 0.1 rad/sec. and to ensure stability in the presence of higher frequency elastic modes, the design model should include at least the first three flexible modes together with the rigid body modes.

Sundararajan, N.

Tests of Gravitational Symmetries with Pulsar Binary J1713+0747

Symmetries play a fundamental role in modern theories of gravity. The strong equivalence principle (SEP) constitutes a collection of gravitational symmetries which are all implemented by general relativity. Alternative theories, however, are generally expected to violate some aspects of SEP. We test three aspects of SEP using observed change rates in the orbital period and eccentricity of binary pulsar J1713+0747: (1) the gravitational constant’s constancy as part of locational invariance of gravitation; (2) the universality of free fall (UFF) for strongly self-gravitating bodies; (3) the post-Newtonian parameter ˆα3 in gravitational Lorentz invariance. Based on the pulsar timing result of the combined data set from the North American Nanohertz Gravitational Observatory and the European Pulsar Timing Array, we find G˙ /G = (−0.1 ± 0.9) × 10−12 yr−1, which is weaker than Solar system limits, but applies for strongly self-gravitating objects. Furthermore, we obtain an improved test for a UFF violation by a strongly self-gravitating mass falling in the gravitational field of our Galaxy, with a limit of |Delta| < 0.002 (95 per cent C.L.). Finally, we derive an improved limit on the self-acceleration of a gravitationally bound rotating body, to a preferred reference frame in the Universe, with −3 × 10−20 < ˆα3 < 4 × 10−20 (95 per cent C.L.). These results are based on direct UFF and ˆα3 tests using pulsar binaries, and they overcome various limitations of previous tests of this kind.

W W Zhu

Separated flows near the nose of a body of revolution

The solution of the Navier-Stokes equations for the problem of cross-flow separataion about a deforming cylinder was achieved by iteration. It was shown that the separation starts at the rear stagnation point and the point of primary separation moves upstram along the cylinder surface. A general method of linear stability analysis for nonparallel external flows was constructed, which consists of representing the eigenfunctions with complete orthogonal sets and forms characteristic equations with the Galerkin method. The method was applied to the Kovasznay flow which is an exact solution of the Navier-Stokes equation. The results show that when the critical parameter is exceeded, there are only a few isolated unstable eigen-frequencies. Another exact solution is shown to be absolutely and monotonically stable with respect to infinitesimal disturbances of all frequencies. The flow is also globally, asymptotically, and monotonically stable in the mean with respect o three-dimensional disturbances. This result forms the sound foundation of rigorous stability analysis for nonparallel flows, and provides an invaluable test ground for future studies of nonparallel flows in which the basic states do not posses exact solutions. The application of this method to the study of the formation of spiral vorticies near the nose of a rotating body of revolution is underway. The same method will be applied to the stability analysis of reversed flow over a plate with suction.

Lin, S. P.

Trajectory Design Employing Convex Optimization for Landing on Irregularly Shaped Asteroids

Mission proposals that land on asteroids are becoming popular. However, in order to have a successful mission the spacecraft must reliably and softly land at the intended landing site. The problem under investigation is how to design a fuel-optimal powered descent trajectory that can be quickly computed on- board the spacecraft, without interaction from ground control. An optimal trajectory designed immediately prior to the descent burn has many advantages. These advantages include the ability to use the actual vehicle starting state as the initial condition in the trajectory design and the ease of updating the landing target site if the original landing site is no longer viable. For long trajectories, the trajectory can be updated periodically by a redesign of the optimal trajectory based on current vehicle conditions to improve the guidance performance. One of the key drivers for being completely autonomous is the infrequent and delayed communication between ground control and the vehicle. Challenges that arise from designing an asteroid powered descent trajectory include complicated nonlinear gravity fields, small rotating bodies and low thrust vehicles. There are two previous studies that form the background to the current investigation. The first set looked in-depth at applying convex optimization to a powered descent trajectory on Mars with promising results.1, 2 This showed that the powered descent equations of motion can be relaxed and formed into a convex optimization problem and that the optimal solution of the relaxed problem is indeed a feasible solution to the original problem. This analysis used a constant gravity field. The second area applied a successive solution process to formulate a second order cone program that designs rendezvous and proximity operations trajectories.3, 4 These trajectories included a Newtonian gravity model. The equivalence of the solutions between the relaxed and the original problem is theoretically established. The proposed solution for designing the asteroid powered descent trajectory is to use convex optimization, a gravity model with higher fidelity than Newtonian, and an iterative solution process to design the fuel optimal trajectory. The solution to the convex optimization problem is the thrust profile, magnitude and direction, that will yield the minimum fuel trajectory for a soft landing at the target site, subject to various mission and operational constraints. The equations of motion are formulated in a rotating coordinate system and includes a high fidelity gravity model. The vehicle's thrust magnitude can vary between maximum and minimum bounds during the burn. Also, constraints are included to ensure that the vehicle does not run out of propellant, or go below the asteroid's surface, and any vehicle pointing requirements. The equations of motion are discretized and propagated with the trapezoidal rule in order to produce equality constraints for the optimization problem. These equality constraints allow the optimization algorithm to solve the entire problem, without including a propagator inside the optimization algorithm.

Pinson, Robin M.

Robust Implicit Adaptive Low Rank Time-Stepping Methods for Matrix Differential Equations

In this work, we develop implicit rank-adaptive schemes for time-dependent matrix differential equations. The dynamic low rank approximation (DLRA) is a well-known technique to capture the dynamic low rank structure based on Dirac–Frenkel time-dependent variational principle. In recent years, it has attracted a lot of attention due to its wide applicability. Our schemes are inspired by the three-step procedure used in the rank adaptive version of the unconventional robust integrator (the so called BUG integrator) (Ceruti et al. in BIT Numer Math 62(4):1149–1174, 2022) for DLRA. First, a prediction (basis update) step is made computing the approximate column and row spaces at the next time level. Second, a Galerkin evolution step is invoked using an implicit solves for the small core matrix. Finally, a truncation is made according to a prescribed error threshold. Since the DLRA is evolving the differential equation projected on to the tangent space of the low rank manifold, the error estimate of the BUG integrator contains the tangent projection (modeling) error which cannot be easily controlled by mesh refinement. This can cause convergence issue for equations with cross terms. To address this issue, we propose a simple modification, consisting of merging the row and column spaces from the explicit step truncation method together with the BUG spaces in the prediction step. In addition, we propose an adaptive strategy where the BUG spaces are only computed if the residual for the solution obtained from the prediction space by explicit step truncation method, is too large. Here, we prove stability and estimate the local truncation error of the schemes under assumptions. We benchmark the schemes in several tests, such as anisotropic diffusion, solid body rotation and the combination of the two, to show robust convergence properties.

97 MATHEMATICS AND COMPUTING

Deep learning of structural morphology imaged by scanning X-ray diffraction microscopy

Scanning X-ray nanodiffraction microscopy is a powerful technique for spatially resolving nanoscale structural morphologies by diffraction contrast. One of the critical challenges in experimental nanodiffraction data analysis is posed by the convergence angle of nanoscale focusing optics which creates simultaneous dependency of the far-field scattering data on three independent components of the local strain tensor-corresponding to dilation and two potential rigid body rotations of the unit cell. All three components are in principle resolvable through a spatially mapped sample tilt series; however, traditional data analysis is computationally expensive and prone to artifacts. In this study, we implement NanobeamNN, a convolutional neural network specifically tailored to the analysis of scanning probe X-ray microscopy data. NanobeamNN learns lattice strain and rotation angles from simulated diffraction of a focused X-ray nanobeam by an epitaxial thin film and can directly make reasonable predictions on experimental data without the need for additional fine-tuning. We demonstrate that this approach represents a significant advancement in computational speed over conventional methods, as well as a potential improvement in accuracy over the current standard.

Luo, Aileen [Cornell Univ., Ithaca, NY (United Sta

Estimation and detection of signals in multiplicative noise

A class of detection-estimation problems on matrix Lie groups is defined in which the observation noise is multiplicative in nature. By examining the differential versions of the hypotheses, which are bilinear in nature, it is possible to derive the relevant likelihood ratio formula and the associated optimal estimation equations for the signal given the observations and the assumption that the signal is present. These estimation equations are of interest in their own right, in that they represent a finite dimensional optimal solution to a nonlinear estimation problem and can be viewed as consisting of a Kalman-Bucy filter along with the on-line computation of the solution of the associated Riccati equation, which is driven by the observations. The usefulness of these results is illustrated via an example concerning the detection of an actuator failure in a rigid body rotational control system.

Willsky, A. S.

Spacecraft control section for the improved Small Astronomy Satellite (SAS)

The upgraded spacecraft control section for the Small Astronomy Satellite is able to point its thrust axis to any direction in space; it can also spin or slow its outer body rotation to zero for star-locked pointing of side viewing experiments. A programmable telemetry system and delayed command system enhance the inherent capability of a spacecraft designed to be used for a variety of experiments, each of which can be built independently and attached just prior to final acceptance testing and launch. The design of this new spacecraft, whose first launch is scheduled for 1975, is provided in sufficient detail to permit the reader to ascertain its suitability for specific experiments. A summary of the spacecraft characteristics, project reliability requirements, and environmental test conditions are included in the appendices.

Townsend, M. R.

The standardized functional support sectional for the Small Astronomy Satellite (SAS)

The standardized functional support section for the improved Small Astronomy Satellite (SAS) spacecraft, which can be used virtually without change for a wide variety of experimental packages and missions, is described. This functional support section makes the spacecraft remarkably flexible for a small satellite. Able to point its thrust axis to any direction in space, it can also spin or slow its outer body rotation to zero for star- or earth-locked pointing of side-viewing experiments. It features a reprogrammable telemetry system, a delayed command system, and an improved control system. Experiments can be built independently and attached to the SAS spacecraft just prior to final acceptance testing and launch. The spacecraft subsystems are described in detail. Included are a summary of the spacecraft characteristics, special design considerations, project reliability requirements, and environmental test conditions. It is intended that this new functional support section afford virtual off-the-shelf availability of the SAS spacecraft to independently built experiments, thus providing quick response time and minimum cost in meeting a wide variety of experimenter needs.

Townsend, M. R.

Spacecraft control section for the improved Small Astronomy Satellite /SAS-C/

The upgraded spacecraft control section for the Small Astronomy Satellite (SAS-C) incorporates a remarkable amount of flexibility for a small satellite. Able to point its thrust axis to any direction in space, it can also spin or slow its outer body rotation to zero for star-locked pointing of side viewing experiments. A programmable telemetry system and delayed command system enhance the inherent capability of a spacecraft designed to be used for a variety of experiments, each of which can be built independently and attached just prior to final acceptance testing and launch. The design of this new spacecraft, whose first launch is scheduled for 1975, is provided in sufficient detail to permit the reader to ascertain its suitability for specific experiments.

Townsend, J. R.

A generalized tensor formulation of atmosphere and seas dynamics

A generalized mathematical model was developed for simulation of the dynamics and transport of both the atmosphere and seas. A nearly horizontal bottom coordinate surface conforms to the land-to-air interface and the sea-floor-to-water interface, which simplifies computations. General vertical motion of the other quasi-horizontal coordinate surfaces is allowed; external gravity waves can be represented by the top coordinate surface, and meteorological fronts and inversion layers in the atmosphere and refractive layers in the seas can be represented with enhanced resolution by the internal quasi-horizontal coordinate surfaces. A tensor reformulation of the standard subgrid mixing theory departs significantly from the standard theory in allowing, as a solution under adiabatic conditions, rigid-body rotation of the atmosphere.

Avis, L. M.