The effects of viscous friction on axial rotation of celestial bodies.
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Kopal, Z.↗
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Trajectories of ballistic impact ejecta on a rotating Earth
On an airless, slowly rotating planetary body like the Moon, ejecta particles from an impact follow simple ballistic trajectories. If gaseous interactions in the fireball are ignored, ejecta particles follow elliptical orbits with the center of the planetary body at one focus until they encounter the surface at the point of reimpact. The partial elliptical orbit of the ejecta particle lies in a plane in inertial (galactic) coordinates. Because of the slow rotation rate (for example, 360 degrees/28 days for the Moon), the intersection of the orbital plane and the surface remains nearly a great circle during the flight time of the ejecta. For this reason, lunar rays, representing concentrations of ejecta with the same azimuth but different velocities and/or ejecta angles, lie essentially along great circles. Ejecta from airless but more rapidly rotating bodies will follow more complicated, curving trajectories when plotted in the coordinate frame of the rotating planet or viewed as rays on the planetary surface. The curvature of trajectories of ejecta particles can be treated as a manifestation of the Coriolis effect, with the particles being accelerated by Coriolis pseudoforces. However, it is more straightforward to calculate the elliptical orbit in inertial space and then determine how far the planet rotates beneath the orbiting ejecta particle before reimpact. The Earth's eastward rotation affects ballistic ejecta in two ways: (1) the eastward velocity component increases the velocity of eastbound ejecta and reduces the velocity of westbound ejecta; and (2) the Earth turns underneath inflight ejecta, so that although the latitude of reimpact is not changed, the longitude is displaced westward, with the displacement increasing as a function of the time the ejecta remains aloft.
Alvarez, W.↗
Translational and rotational motion of a body entering the martian atmosphere <translations- und rotationsbewegung eines in die marsatmosphaere eintauchenden koerpers<.
Rotational, precessional and nutational motion of body entering Mars atmosphere in vertical and oblique directions
ROTATING SPHERE↗
Sensorimotor integration in human postural control
It is generally accepted that human bipedal upright stance is achieved by feedback mechanisms that generate an appropriate corrective torque based on body-sway motion detected primarily by visual, vestibular, and proprioceptive sensory systems. Because orientation information from the various senses is not always available (eyes closed) or accurate (compliant support surface), the postural control system must somehow adjust to maintain stance in a wide variety of environmental conditions. This is the sensorimotor integration problem that we investigated by evoking anterior-posterior (AP) body sway using pseudorandom rotation of the visual surround and/or support surface (amplitudes 0.5-8 degrees ) in both normal subjects and subjects with severe bilateral vestibular loss (VL). AP rotation of body center-of-mass (COM) was measured in response to six conditions offering different combinations of available sensory information. Stimulus-response data were analyzed using spectral analysis to compute transfer functions and coherence functions over a frequency range from 0.017 to 2.23 Hz. Stimulus-response data were quite linear for any given condition and amplitude. However, overall behavior in normal subjects was nonlinear because gain decreased and phase functions sometimes changed with increasing stimulus amplitude. "Sensory channel reweighting" could account for this nonlinear behavior with subjects showing increasing reliance on vestibular cues as stimulus amplitudes increased. VL subjects could not perform this reweighting, and their stimulus-response behavior remained quite linear. Transfer function curve fits based on a simple feedback control model provided estimates of postural stiffness, damping, and feedback time delay. There were only small changes in these parameters with increasing visual stimulus amplitude. However, stiffness increased as much as 60% with increasing support surface amplitude. To maintain postural stability and avoid resonant behavior, an increase in stiffness should be accompanied by a corresponding increase in damping. Increased damping was achieved primarily by decreasing the apparent time delay of feedback control rather than by changing the damping coefficient (i.e., corrective torque related to body-sway velocity). In normal subjects, stiffness and damping were highly correlated with body mass and moment of inertia, with stiffness always about 1/3 larger than necessary to resist the destabilizing torque due to gravity. The stiffness parameter in some VL subjects was larger compared with normal subjects, suggesting that they may use increased stiffness to help compensate for their loss. Overall results show that the simple act of standing quietly depends on a remarkably complex sensorimotor control system.
NASA Discipline Neuroscience↗
Regularization of the restricted problem of four bodies.
Regularization of restricted three-body problem extended to case where three primaries of any mass revolve in circular orbits around common center of mass and fourth body of infinitesimal mass moves in their field
CIRCULAR ORBIT↗
The rotation of Uranus
The rotation rate of Uranus is investigated by measuring the tilts of reflected Fraunhofer lines observed through a slit spectrograph. The data obtained are corrected for the effect of astronomical seeing, and the data-reduction procedures are outlined in detail. Observations are discussed which indicate that the planet's pole of rotation is parallel to the pole of its satellites' orbits and that Uranus may not rotate as a solid body. A rotational period of 15.57 + or - 0.80 hr is derived for northern midlatitudes on Uranus by adopting a planetary diameter of 51,800 + or - 600 km. Possible sources of small systematic errors are briefly considered.
Brown, R. A.↗
Flow over a slender body of revolution at supersonic velocities
The theory of small disturbances is applied to the calculation of the pressure distribution and drag of a closed body of revolution traveling at supersonic speeds. It is shown that toward the rear of the body the shape of the pressure distribution is similar to that for subsonic flow. For fineness ratios between 10 and 15 the theoretical wave drag is of the same order as probable values of the frictional drag.
FLOW VELOCITY, HIGH-SUPERSONIC↗
Reactive Hydrodynamics in Rotating Spherical and Cylindrical Geometry
In turbulent spray combustion among many complex interactions between local flow structures called turbulent eddies and droplets are those associated with rotation of droplets. In general, for a complete statistical description of turbulent sprays, consideration of at least four degrees of freedom respectively associated with translational, rotational, vibrational (pulsational), and internal motions of the droplet are needed. Clearly the interactions between all degrees of freedom of the droplets and those for the gaseous background field will be exceedingly complex. For example, one type of interaction between the translational and the rotational velocity of droplets results in droplet helicity, H(d) = w(d).v(d), the significance of which in turbulent spray combustion is yet to be recognized. The role of droplet rotation in turbulent spray combustion modeling and its impact on the evaporation of liquid fuel droplets was recently investigated. Also, the impact of rotation on combustion of solid particles such as is encountered in pulverized coal combustion has been emphasized. The problem of viscous flow around a rotating sphere discussed above also occurs in other areas of physical sciences such as astrophysics and geophysics. Consequently, the subject has been addressed in many classical as well as more recent investigations. According to these investigations, the rotation of a rigid sphere in an otherwise quiescent, unconfined environment results in the motion of the fluid towards the poles. The polar flows from the northern and southern hemispheres move along helical trajectories towards the equatorial plane. Eventually, the polar flows collide at the equatorial plane, thus producing a sheet of rotating fluid that is radially ejected outward on this plane. Therefore, a droplet induces a strained flow field as a result of its rotation. Since the spatial extent of equatorial jets could easily exceed many droplet diameters, interactions between neighboring droplets are enhanced as a result of their rotation. Also, the equatorial jet substantially alters the spherical geometry of the diffusion flame surface that surrounds a rotating droplet. The objective of the research is to gain more knowledge about the hydrodynamics within and around rotating spherical and cylindrical body of fluid, and the behavior of diffusion or premixed flame surfaces that could surround such symmetric body of rotating fluid.
Sohrab, Siavash H.↗
Probable Rotation States of Rocket Bodies in Low Earth Orbit
In order for Active Debris Removal to be accomplished, it is critically important to understand the probable rotation states of orbiting, spent rocket bodies. As compared to the question of characterizing small unresolved debris, in this problem there are several advantages: (1) objects are of known size, mass, shape and color, (2) they have typically been in orbit for a known period of time, (3) they are large enough that resolved images may be obtainable for verification of predicted orientation, and (4) the dynamical problem is simplified to first order by largely cylindrical symmetry. It is also nearly certain for realistic rocket bodies that internal friction is appreciable in the case where residual liquid or, to a lesser degree, unconsolidated solid fuels exist. Equations of motion have been developed for this problem in which internal friction as well as torques due to solar radiation, magnetic induction, and gravitational gradient are included. In the case of pure cylindrical symmetry, the results are compared to analytical predictions patterned after the standard approach for analysis of symmetrical tops. This is possible because solar radiation and gravitational torques may be treated as conservative. Agreement between results of both methods ensures their mutual validity. For monotone symmetric cylinders, solar radiation torque vanishes if the center of mass resides at the geometric center of the object. Results indicate that in the absence of solar radiation effects, rotation states tend toward an equilibrium configuration in which rotation is about the axis of maximum inertia, with the axis of minimum inertia directed toward the center of the earth. Solar radiation torque introduces a modification to this orientation. The equilibrium state is asymptotically approached within a characteristic timescale given by a simple ratio of relevant characterizing parameters for the body in question. Light curves are simulated for the expected asymptotic final rotation states of model objects, and these are compared to data derived from physical models of the same objects, tested in the Optical Measurements Center at JSC. Comparison to relevant light curves from actual orbiting rocket bodies are also performed, and diagnostic features of such curves are examined.
Ojakangas, Gregory W.↗
Ejecta patterns diagnostic of planetary rotations
A new scheme for determining a body's rotational history from the geological record is presented. Trajectories of ejecta on a rotating object are affected by the Coriolis effect in a manner characteristic of the direction and speed of the object's spin. This information is registered on the surface in the form of debris deposits and ray patterns, and can be interpreted by comparing photographs of the planet's surface with specified paradigms. This approach has the advantage of being independent of the body's internal structure and of relating its rotational history directly to its cratering chronology. This approach could be used, for example, to date the despinning of Mercury relative to its latest bombardment.
Dobrovolskis, A.↗
On the parametrization of the three-dimensional rotation group.
Parameterization of group of rotations of Euclidean three-dimensional space applied to integration of rigid body motion equations
MOTION EQUATION↗
Lunar rotational dissipation in solid body and molten core
Analyses of Lunar Laser ranges Shaw a displacement in direction of the Moon's pole of rotation which indicates that strong dissipation is acting on the rotation.
Thermal history earth-moon systems evolutions tide↗
Physical Phenomena in Containerless Glass Processing
An investigation into the various physical phenomena of importance in the space experiments is under way. Theoretical models of thermocapillary flow in drops, thermal migration of bubbles and droplets, the motion of bubbles inside drops, and the migration of bubbles in rotating liquid bodies are being developed. Experiments were conducted on the migration of bubbles and droplets to the axis of a rotating liquid body, and the rise of bubbles in molten glass. Also, experiments on thermocapillary motion in silicone oils as well as glass melts were performed. Experiments are currently being conducted on the migration of bubbles in a thermal gradient, and on their motion inside unconstrained liquid drops in a rotating liquid.
Subramanian, R. S.↗
Optical Navigation for Autonomous Approach of Small Unknown Bodies
State of the practice in navigation around small celestial bodies heavily relies on ground sup- port and human skill, in particular, for perception-based operations such as optical navigation and mapping. This leads to longer duration and more complex mission operations and sub- sequently higher cost. Furthermore, it imposes limitations for certain missions such as fast fly-bys or multi-agent operations. In this work, we present an autonomous navigation strat- egy suitable for approaching small unexplored bodies. During the approach, we estimate the body’s physical properties as well as the spacecraft’s relative trajectory and associated un- certainties. The autonomous navigation strategy, which is solely based on optical measure- ments, begins as soon as the body becomes resolved in the navigation camera and terminates at the start of proximity operations, when the spacecraft makes its first trajectory correction to stay in the vicinity of the body. Our strategy uses multiple image-processing algorithms: light-curve analysis for estimating the target body’s rotation rate, Shape-from-Silhouette for reconstructing the 3D shape and estimating its rotation pole, and feature tracking tailored to Small-Body images for estimating relative navigation parameters. We used the Mission Analysis, Operations, and Navigation Toolkit Environment (MONTE) developed by the Jet Propulsion Laboratory to evaluate the feasibility of this multi-phase navigation strategy using simulated images of an approach trajectory. We used the Rosetta mission data to generate photorealistic images to characterise the performance of this approach. This work is based on the assumptions that the spacecraft attitude is known, the body is a principal-axis rotator, a-priori estimates of ephemerides and scale are available, and the body is observed from a zero sun phase only during initial approach. Preliminary results show orbit determination performance that is on par with the human navigation from the Rosetta mission; albeit with a 1% bias in spacecraft-target radial distance estimate. The bias error is likely due to the robustness and accuracy of the visual tracking under dynamic lighting conditions and per- spective changes, which decrease accuracy.
Villa, Jacopo↗
Method for Forming MEMS-Based Spinning Nozzle
A nozzle body and assembly for delivering atomized fuel to a combustion chamber. The nozzle body is rotatably mounted onto a substrate. One or more curvilinear fuel delivery channels are in flow communication with an internal fuel distribution cavity formed in the nozzle body. Passage of pressurized fuel through the nozzle body causes the nozzle body to rotate. Components of the nozzle assembly are formed of silicon carbide having surfaces etched by deep reactive ion etching utilizing MEMS technology. A fuel premix chamber is carried on the substrate in flow communication with a supply passage in the nozzle body.
Robert S Okojie↗
MEMS-Based Spinning Nozzle
A nozzle body and assembly for delivering atomized fuel to a combustion chamber. The nozzle body is rotatably mounted onto a substrate. One or more curvilinear fuel delivery channels are in flow communication with an internal fuel distribution cavity formed in the nozzle body. Passage of pressurized fuel through the nozzle body causes the nozzle body to rotate. Components of the nozzle assembly are formed of silicon carbide having surfaces etched by deep reactive ion etching utilizing MEMS (micro-electro-mechanical systems) technology. A fuel premix chamber is carried on the substrate in flow communication with a supply passage in the nozzle body.
Robert S Okojie↗
A general-purpose approach to computer-aided dynamic analysis of a flexible helicopter
A general purpose mathematical formulation is described for dynamic analysis of a helicopter consisting of flexible and/or rigid bodies that undergo large translations and rotations. Rigid body and elastic sets of generalized coordinates are used. The rigid body coordinates define the location and the orientation of a body coordinate frame (global frame) with respect to an inertial frame. The elastic coordinates are introduced using a finite element approach in order to model flexible components. The compatibility conditions between two adjacent elements in a flexible body are imposed using a Boolean matrix, whereas the compatibility conditions between two adjacent bodies are imposed using the Lagrange multiplier approach. Since the form of the constraint equations depends upon the type of kinematic joint and involves only the generalized coordinates of the two participating elements, then a library of constraint elements can be developed to impose the kinematic constraint in an automated fashion. For the body constraints, the Lagrange multipliers yield the reaction forces and torques of the bodies at the joints. The virtual work approach is used to derive the equations of motion, which are a system of differential and algebraic equations that are highly nonlinear. The formulation presented is general and is compared with hard-wired formulations commonly used in helicopter analysis.
Agrawal, Om P.↗