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At least 127 records · Page 7

Formulation and application of Russell's method

It is shown that the numerical technique of Russell's momentum approach can be derived by using Hamilton's principle and Vance's numerical scheme. It results in a set of first order differnce equations for solving the angular velocities. The numerical examples show that the method is reliable. The algorithm is modified next to perform the analysis of N-body systems with closed loop topology. To increase the formulation flexibility, the equations of motion are represented by using Cartesian coordinates and Lagrange multipliers. The algorithm consists of two parts, Vance's scheme and an unconstrained minimization. The Vance's scheme is used to find the angular velocities, and the unconstrained minimization is applied to provide the correct angular displacements. The proposed scheme is further extended to find the design sensitivity of an N-body system with closed loop configuration, and to carry out the design optimization as well. The numerical example of a small-scaled mechanical system is presented to verify the proposed formulation.

Hou, J. W.↗

A method of determining attitude from magnetometer data only

Presented here is a new algorithm to determine attitude using only magnetometer data under the following conditions: (1) internal torques are known and (2) external torques are negligible. Torque-free rotation of a spacecraft in thruster firing acquisition phase and its magnetic despin in the B-dot mode give typical examples of such situations. A simple analytical formula has been derived in the limiting case of a spacecraft rotating with constant angular velocity. The formula has been tested using low-frequency telemetry data for the Earth Radiation Budget Satellite (ERBS) under normal conditions. Observed small oscillation of body-fixed components of the angular velocity vector near their mean values result in relatively minor errors of approximately 5 degrees. More significant errors come from processing digital magnetometer data. Higher resolution of digitized magnetometer measurements would significantly improve the accuracy of this deterministic scheme. Tests of the general version of the developed algorithm for a free-rotating spacecraft and for the B-dot mode are in progress.

Natanson, G. A.↗

The molecular complexes in Orion

Line emission from CO at 2.6 mm is observed over an area of 28 square degrees in the Orion region. Most of the emission comes from two giant molecular complexes, roughly associated with Ori B and Ori A. The latter provides the best example of a giant molecular complex at the end of a sequence of OB association subgroups of decreasing age. This complex is apparently rotating with an angular velocity 4.5 by 10 to the -15th power per sec, but in a direction opposed to the Galactic rotation. The apparently denser parts of the cloud are rotating at a somewhat greater angular velocity. The total mass of the molecular gas derived from the observations is 200,000 solar masses, implying that roughly half the matter in this region is in the form of molecular hydrogen.

Kutner, M. L.↗

Contribution to the ideal efficiency of screw propellers

The stipulation of best thrust distribution is applied to the annular elements of the screw propeller with infinitely many blades in frictionless, incompressible flow and an ideal jet propulsion system derived possessing hyperbolic angular velocity distribution along the blade radius and combining the advantage of uniform thrust distribution over the section with minimum slipstream and rotation losses. This system is then compared with a propeller possessing the same angular velocity at all blade elements and the best possible thrust distribution secured by means of an induced efficiency varying uniformly over the radius. Lastly, the case of the lightly loaded propeller also is discussed.

Hoff, Wilhelm↗

Co-Spin With Symmetry Axis Stabilization, and De-Spin for Asteroid Capture

Consideration is given to attitude control associated with capturing a free-flying asteroid using an axisymmetric spacecraft. Asymptotically stable controllers are designed to align the spacecraft axis of symmetry with a line of descent that is fixed in the asteroid, and to eliminate all relative angular velocity before capture takes place. An analytical expression is presented for the torque required to maintain alignment of the axes of symmetry of the spacecraft and an axisymmetric asteroid. After the asteroid is securely captured, the angular velocity of the rigid composite body relative to an inertial frame is arrested; we present a controller that is asymptotically stable and stays within specified thrust limits.

Shen, Haijun↗

Premotor neurons encode torsional eye velocity during smooth-pursuit eye movements

Responses to horizontal and vertical ocular pursuit and head and body rotation in multiple planes were recorded in eye movement-sensitive neurons in the rostral vestibular nuclei (VN) of two rhesus monkeys. When tested during pursuit through primary eye position, the majority of the cells preferred either horizontal or vertical target motion. During pursuit of targets that moved horizontally at different vertical eccentricities or vertically at different horizontal eccentricities, eye angular velocity has been shown to include a torsional component the amplitude of which is proportional to half the gaze angle ("half-angle rule" of Listing's law). Approximately half of the neurons, the majority of which were characterized as "vertical" during pursuit through primary position, exhibited significant changes in their response gain and/or phase as a function of gaze eccentricity during pursuit, as if they were also sensitive to torsional eye velocity. Multiple linear regression analysis revealed a significant contribution of torsional eye movement sensitivity to the responsiveness of the cells. These findings suggest that many VN neurons encode three-dimensional angular velocity, rather than the two-dimensional derivative of eye position, during smooth-pursuit eye movements. Although no clear clustering of pursuit preferred-direction vectors along the semicircular canal axes was observed, the sensitivity of VN neurons to torsional eye movements might reflect a preservation of similar premotor coding of visual and vestibular-driven slow eye movements for both lateral-eyed and foveate species.

Non-NASA Center↗

Dynamics of the G-excess illusion

The G-excess illusion is increasingly recognized as a cause of aviation mishaps especially when pilots perform high-speed, steeply banked turns at low altitudes. Centrifuge studies of this illusion have examined the perception of subject orientation and/or target displacement during maintained hypergravity with the subject's head held stationary. The transient illusory perceptions produced by moving the head in hypergravity are difficult to study onboard centrifuges because the high angular velocity ensures the presence of strong Coriolis cross-coupled semicircular canal effects that mask immediate transient otolith-organ effects. The present study reports perceptions following head movements in hypergravity produced by high-speed aircraft maintaining a banked attitude with low angular velocity to minimize cross-coupled effects. Methods: Fourteen subjects flew on the NASA KC-135 and were exposed to resultant gravity forces of 1.3, 1.5, and 1.8 G for 3 minute periods. On command, seated subjects made controlled head movements in roll, pitch, and yaw at 30 second intervals both in the dark and with faint targets at a distance of 5 feet. Results: head movement produced transient perception of target displacement and velocity at levels as low as 1.3 G. Reports of target velocity without appropriate corresponding displacement were common. At 1.8 G when yaw head movements were made from a face down position, 4 subjects reported oscillatory rotational target displacement with fast and slow alternating components suggestive of torsional nystagmus. Head movements evoked symptoms of nausea in most subjects, with 2 subjects and 1 observer vomiting. Conclusions: The transient percepts present conflicting signals, which introduced confusion in target and subject orientation. Repeated head movements in hypergravity generate nausea by mechanisms distinct from cross-coupled Coriolis effects.

Baylor, K. A.↗

On the supposed anticorrelation of solar polar and equatorial rotation rates

The anticorrelation between two of the three parameters used to calculate the angular velocity of the sun's differential rotation is here said to be due to numerical coupling. A computer simulation technique shows that the relationship between the two parameters is caused by the effect of noise on the least-squares analysis used to obtain the three parameters used to determine the angular velocity in terms of the heliographic latitude. The computer simulation technique is described. The supposed anticorrelation had been used to infer that variations of the sun's polar and equatorial rotation rates are anticorrelated.

Duvall, T. L., Jr.↗

The motion and stability of a dual spin satellite during the momentum wheel spin-up maneuver

The stability of a dual-spin satellite system during the momentum wheel spin-up maneuver is treated both analytically and numerically. The dual-spin system consists of: a slowly rotating or despun main-body; a momentum wheel (or rotor) which is accelerated by a torque motor to change its initial angular velocity relative to the main part to some high terminal value; and a nutation damper. A closed form solution for the case of a symmetrical satellite indicates that when the nutation damper is physically constrained for movement (i.e. by use of a mechanical clamp) the magnitude of the vector sum of the transverse angular velocity components remains bounded during the wheel spin-up under the influence of a constant motor torque. The analysis is extended to consider such effects as: the motion of the nutation damper during spin-up; a non-uniform motor torque; and the effect of a non-symmetrical mass distribution in the main spacecraft and the rotor. An approximate analytical solution using perturbation techniques is developed for the case of a slightly asymmetric main spacecraft.

Bainum, P. M.↗

The motion and stability of a dual-spin satellite during the momentum wheel spin-up maneuver.

The stability of a dual-spin satellite system during the momentum wheel spin-up maneuver is treated both analytically and numerically. The dual-spin system consists of a slowly rotating or despun main body, a momentum wheel (or rotor) which is accelerated by a torque motor to change its initial angular velocity relative to the main part to some high terminal value, and a nutation damper. A closed-form solution for the case of a symmetrical satellite indicates that when the nutation damper is physically constrained from movement (i.e., by use of a mechanical clamp) the magnitude of the vector sum of the transverse angular velocity components remains bounded during the wheel spin-up under the influence of a constant motor torque. The analysis is extended to consider such effects as the motion of the nutation damper during spin-up, and the effect of a nonsymmetrical mass distribution.

Sen, S.↗

Dynamics of spin stabilized spacecraft during deployment of telescoping appendages

The dynamics of a spin stabilized spacecraft with telescoping appendages are treated both analytically and numerically. Two types of telescoping appendages are considered: (a) where an end mass is mounted at the end of an (assumed) massless boom; and (b) where the appendage is assumed to consist of a uniformly distributed homogeneous mass throughout its length. For the telescoping system Eulerian equations of motion are developed. During all deployment sequences it is assumed that the transverse component of angular momentum is much smaller than the component along the major spin axis. Closed form analytical solutions for the time response of the transverse components of angular velocities are obtained when the spacecraft hub has a nearly spherical mass distribution. For the more general case, a series solution is obtained and this solution is limited by its radius of convergence. The comparison of the different approximate analytical methods with numerical integration results are studied and it is observed that the oscillatory nature of the responses of the transverse angular velocity components reduces rapidly with faster extension rates.

Sellappan, R.↗

Rotational Inversion from Global Solar Oscillations

The degree to which various sets of solar oscillations can resolve the solar internal rotation was investigated. Genuine observations were simulated by the following procedure; first an artificial angular velocity was invented, and from it the rotational splitting of a set of normal modes was calculated; to that was added some random noise. The result was treated as artificial data and an attempt to recover the rotation law by using the Backus-Gilbert optimal averaging procedure was made. Neither the original rotation law nor the amount of noise that had been added was known. The conclusion was compared with the actual artificial angular velocity.

Christensen-Dalsgaard, J.↗

Methodology issues concerning the accuracy of kinematic data collection and analysis using the ariel performance analysis system

Kinematics, the study of motion exclusive of the influences of mass and force, is one of the primary methods used for the analysis of human biomechanical systems as well as other types of mechanical systems. The Anthropometry and Biomechanics Laboratory (ABL) in the Crew Interface Analysis section of the Man-Systems Division performs both human body kinematics as well as mechanical system kinematics using the Ariel Performance Analysis System (APAS). The APAS supports both analysis of analog signals (e.g. force plate data collection) as well as digitization and analysis of video data. The current evaluations address several methodology issues concerning the accuracy of the kinematic data collection and analysis used in the ABL. This document describes a series of evaluations performed to gain quantitative data pertaining to position and constant angular velocity movements under several operating conditions. Two-dimensional as well as three-dimensional data collection and analyses were completed in a controlled laboratory environment using typical hardware setups. In addition, an evaluation was performed to evaluate the accuracy impact due to a single axis camera offset. Segment length and positional data exhibited errors within 3 percent when using three-dimensional analysis and yielded errors within 8 percent through two-dimensional analysis (Direct Linear Software). Peak angular velocities displayed errors within 6 percent through three-dimensional analyses and exhibited errors of 12 percent when using two-dimensional analysis (Direct Linear Software). The specific results from this series of evaluations and their impacts on the methodology issues of kinematic data collection and analyses are presented in detail. The accuracy levels observed in these evaluations are also presented.

Wilmington, R. P.↗

Collision detection for spacecraft proximity operations

A new collision detection algorithm has been developed for use when two spacecraft are operating in the same vicinity. The two spacecraft are modeled as unions of convex polyhedra, where the resulting polyhedron many be either convex or nonconvex. The relative motion of the two spacecraft is assumed to be such that one vehicle is moving with constant linear and angular velocity with respect to the other. Contacts between the vertices, faces, and edges of the polyhedra representing the two spacecraft are shown to occur when the value of one or more of a set of functions is zero. The collision detection algorithm is then formulated as a search for the zeros (roots) of these functions. Special properties of the functions for the assumed relative trajectory are exploited to expedite the zero search. The new algorithm is the first algorithm that can solve the collision detection problem exactly for relative motion with constant angular velocity. This is a significant improvement over models of rotational motion used in previous collision detection algorithms.

Vaughan, Robin M.↗

Mercury's core - The effect of obliquity on the spin-orbit constraints

Constraints were previously placed on various properties of a Mercurian liquid core for compatibility with Mercury's escape from the stable spin-orbit resonance with the spin angular velocity equal to twice the orbital mean motion (the 2n resonance), under the assumption that the planet's obliquity was nearly zero at the time of resonance passage. Capture probabilities at arbitrary nonzero obliquities for the 2n resonance are determined for the cases where the core is strongly or weakly coupled to the mantle. It is found that the capture probabilities are reduced to below unity for all core-fluid viscosities in the weak-coupling limit, but are almost unchanged in the strong-coupling limit. The reduction in capture probability is attributed to reduction of the mantle's spin angular velocity by the core-mantle interaction, which would also reduce the obliquity to negligibly small values before the 2n resonance was even reached. It is concluded that the constraints on the core may still be maintained since Mercury most likely passed through the 2n resonance with nearly zero obliquity.

Peale, S. J.↗

A Rotary Flow Channel for Shear Stress Sensor Calibration

A proposed shear sensor calibrator consists of a rotating wheel with the sensor mounted tangential to the rim and positioned in close proximity to the rim. The shear stress generated by the flow at the sensor position is simply tau(sub omega) = (mu)r(omega)/h, where mu is the viscosity of the ambient gas, r the wheel radius, omega the angular velocity of the wheel, and h the width of the gap between the wheel rim and the sensor. With numerical values of mu = 31 (mu)Pa s (neon at room temperature), r = 0.5 m, omega = 754 /s (7200 rpm), and h = 50.8 m, a shear stress of tau(sub omega) = 231 Pa can be generated. An analysis based on one-dimensional flow, with the flow velocity having only an angular component as a function of the axial and radial coordinates, yields corrections to the above simple formula for the curvature of the wheel, flatness of the sensor, and finite width of the wheel. It is assumed that the sensor mount contains a trough (sidewalls) to render a velocity release boundary condition at the edges of the rim. The Taylor number under maximum flow conditions is found to be 62.3, sufficiently low to obviate flow instability. The fact that the parameters entering into the evaluation of the shear stress can be measured to high accuracy with well-defined uncertainties makes the proposed calibrator suitable for a physical standard for shear stress calibration.

Zuckerwar, Allan J.↗