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At least 145 records · Page 8

The dynamics and optimal control of spinning spacecraft with movable telescoping appendages. Part C: Effect of flexibility during boom deployment

The dynamics of a spinning symmetrical spacecraft system during the deployment (or retraction) of flexible boom-type appendages were investigated. The effect of flexibility during boom deployment is treated by modelling the deployable members as compound spherical pendula of varying length (according to a control law). The orientation of the flexible booms with respect to the hub, is described by a sequence of two Euler angles. The boom members contain a flexural stiffness which can be related to an assumed effective restoring linear spring constant, and structural damping which effects the entire system. Linearized equations of motion for this system, when the boom length is constant, involve periodic coefficients with the frequency of the hub spin. A bounded transformation is found which converts this system into a kinematically equivalent one involving only constant coefficients.

Bainum, P. M.↗

Nonlinear compressible convection penetrating into stable layers and producing internal gravity waves

Penetrative convection spanning multiple scale heights is studied within a simple stellar envelope consisting of three layers: a convectively unstable middle layer bounded above and below by stably stratified polytropes. Two-dimensional numerical simulations are used to investigate the fully compressible nonlinear motions that ensue. The cellular flows display prominent downward-directd plumes surrounded by broader regions of upflow. Such asymmetry arises because pressure fluctuations accentuate buoyancy driving in the concentrated plumes and can even lead to weak buoyancy braking in the surrounding ascending flows. As the plumes plunge downward into a region of stable stratification, they serve to excite a broad spectrum of internal gravity waves there. The induced waves are not passive, for they feed back upon the plumes by deflecting them sideways, thereby modulating the amplitude of the convection in time even in the unstable layer. The penetrative motions that billow upward into the upper stable zone are distinctly weaker, and they cascade back downward toward the unstable zone over a broad horizontal scale. The strong excitation of gravity waves by the convection has implications for gradual mixing deep within a star.

Hurlburt, Neal E.↗

The existence and stability of steady circulations in a conditionally symmetrically unstable basic flow

The existence of steady, nonlinear circulations in a flow susceptible to conditionally symmetric instability is studied, treating the latent heating as an energy source which is implicitly related to the motion field. The viscous nonlinear circulations of symmetrical instability are briefly discussed, and an existence theorem for steady, nonlinear symmetric circulations with bounded rates of latent heat release is given. The uniqueness and stability of these circulations are discussed, and some physical interpretations are given.

Xu, Qin↗

Stability of the Halley cometosheath with resistivity and plasma motion

The MHD stability of the cometary inner sheath determined by the balance between the inward Lorentz body force and the outward ion-neutral drag force is investigated by numerically solving the wave equations which include resistivity, plasma motion and plasma pressure with the help of two-point boundary value method. The eigenvalues and the eigenfunctions are obtained numerically by treating the cometary inner sheath as a layer of finite thickness, bounded by the contact surface, that is, the diamagnetic cavity boundary. To gain insight into the problem, certain limiting cases of the wave equations are also discussed. The diamagnetic cavity boundary and the adjacent layer of about 100-km thickness of Comet Halley is found to be unstable. The effects of finite plasma pressure, dissociative recombination, mass loading due to photoionization, resistivity, and plasma motion are found to be stabilizing but are unable to quench the instability completely. Motion of the Halley ionopause has been confirmed by observations.

Srivastava, Krishna M.↗

Aeolian processes aboard a space station: Saltation and particle trajectory analysis

The Carousel wind tunnel (CWT) proposed to study aeolian processes aboard a space station consists of two concentric rotating drums. The space between the two drums comprises the wind tunnel test section. Differential rates of rotation of the two drums would provide a wind velocity with respect to either drum surface. Preliminary results of measured velocity profiles made in a CWT prototype indicate that the wall bounded boundary layer profiles are suitable to simulate flat plate turbulent boundary layer flow. The two dimensional flat plate Cartesian coordinate equations of motion of a particle moving through the air are explained. In order to assess the suitability of CWT in the analysis of the trajectories of windblown particles, a series of calculations were conducted comparing cases for gravity with those of zero gravity. Results from the calculations demonstrate that a wind tunnel of the carousel design could be fabricted to operate in a space station environment and that experiments could be conducted which would yield significant results contributing to the understanding of the physics of particle dynamics.

White, B. R.↗

Aeolian processes aboard a Space Station: Saltation and particle trajectory analysis

The Carousel Wind Tunnel (CWT) proposed to study aeolian processes aboard a Space Station consists of two concentric rotating drums. The space between the two drums comprises the wind tunnel section. Differential rates of rotation of the two drums would provide a wind velocity with respect to either drum surface. Preliminary results of measured velocity profiles made in a CWT prototype indicate that the wall bounded boundary layer profiles are suitable to simuate flat plate turbulent boundary layer flow. The two dimensional flate plate Cartesian coordinate equations of motion of a particle moving through the air are explained. In order to assess the suitability of CWT in the analysis of the trajectories of windblown particles, a series of calculations were conducted comparing cases for gravity with those of zero gravity. Results from the calculations demonstrate that a wind tunnel of the carousel design could be fabricated to operate in a space station environment and that experiments could be conducted which would yield significant results contributing to the understanding of the physics of particle dynamics.

White, Bruce R.↗

Superfluid helium sloshing dynamics induced oscillations and fluctuations of angular momentum, force and moment actuated on spacecraft driven by gravity gradient or jitter acceleration associated with slew motion

The generalized mathematical formulation of sloshing dynamics for partially filled liquid of cryogenic superfluid helium II in dewar containers driven by the gravity gradient and jitter accelerations associated with slew motion for the purpose to perform scientific observation during the normal spacecraft operation are investigated. An example is given with the Advanced X-Ray Astrophysics Facility-Spectroscopy (AXAF-S) for slew motion which is responsible for the sloshing dynamics. The jitter accelerations include slew motion, spinning motion, atmospheric drag on the spacecraft, spacecraft attitude motions arising from machinery vibrations, thruster firing, pointing control of spacecraft, crew motion, etc. Explicit mathematical expressions to cover these forces acting on the spacecraft fluid systems are derived. The numerical computation of sloshing dynamics is based on the non-inertia frame spacecraft bound coordinate, and solve time-dependent, three-dimensional formulations of partial differential equations subject to initial and boundary conditions. The explicit mathematical expressions of boundary conditions to cover capillary force effect on the liquid-vapor interface in microgravity environments are also derived. The formulations of fluid moment and angular moment fluctuations in fluid profiles induced by the sloshing dynamics, together with fluid stress and moment fluctuations exerted on the spacecraft dewar containers have also been derived. Examples are also given for cases applicable to the AXAF-S spacecraft sloshing dynamics associated with slew motion.

Hung, R. J.↗

Research on diabatic initialization

The objective of this research project is to contribute to improvement in the synoptic analyses in the tropics for numerical weather prediction and climate research. In addition to a prediction model, four dimensional data assimilation systems have two principal components. One is objective analysis and the other is initialization. Various methods of objective analysis are designed primarily to analyze the mass and rotational wind fields. Methods of initialization are developed to obtain the irrotational wind and its associated vertical velocity field which are balanced with the mass field and free from meteorological noise. There are essentially three approaches to the problem of initialization: quasi-geostrophic theory, bounded derivative method and nonlinear normal mode method. In the midlatitudes, these approaches generally produce satisfactory results even without diabatic effects for large-scale motions. In the tropics, the situation is quite different from that in the midlatitudes. Because of a small magnitude of the Coriolis parameter and a weak horizontal temperature gradient in the tropics, any method of initialization must incorporate diabatic effects. In fact, it can be said that understanding the problem of diabatic initialization is the key to improving the analysis and weather forecasting in the tropics.

Kasahara, Akira↗

Single-axis gyroscopic motion with uncertain angular velocity about spin axis

A differential game approach is presented for studying the response of a gyro by treating the controlled angular velocity about the input axis as the evader, and the bounded but uncertain angular velocity about the spin axis as the pursuer. When the uncertain angular velocity about the spin axis desires to force the gyro to saturation a differential game problem with two terminal surfaces results, whereas when the evader desires to attain the equilibrium state the usual game with single terminal manifold arises. A barrier, delineating the capture zone (CZ) in which the gyro can attain saturation and the escape zone (EZ) in which the evader avoids saturation is obtained. The CZ is further delineated into two subregions such that the states in each subregion can be forced on a definite target manifold. The application of the game theoretic approach to Control Moment Gyro is briefly discussed.

Singh, S. N.↗

On computing the global time-optimal motions of robotic manipulators in the presence of obstacles

A method for computing the time-optimal motions of robotic manipulators is presented that considers the nonlinear manipulator dynamics, actuator constraints, joint limits, and obstacles. The optimization problem is reduced to a search for the time-optimal path in the n-dimensional position space. A small set of near-optimal paths is first efficiently selected from a grid, using a branch and bound search and a series of lower bound estimates on the traveling time along a given path. These paths are further optimized with a local path optimization to yield the global optimal solution. Obstacles are considered by eliminating the collision points from the tessellated space and by adding a penalty function to the motion time in the local optimization. The computational efficiency of the method stems from the reduced dimensionality of the searched spaced and from combining the grid search with a local optimization. The method is demonstrated in several examples for two- and six-degree-of-freedom manipulators with obstacles.

Shiller, Zvi↗

Instabilities of dynamic thermocapillary liquid layers. I Convective instabilities

A steady shear flow is set up in a planar liquid layer bounded below by a rigid plate, and above by an interface with a passive gas, by imposing a temperature gradient along the layer and driving the motion by thermocapillarity. The thermal-convective instabilities to which this dynamic state is susceptible include stationary longitudinal rolls involving the classical Marangoni instability, and unsteady hydrothermal waves, whose new instability mechanism derives its energy from the horizontal temperature gradients. The thermal stability characteristics for liquid layers with and without return flow profiles are presently given as functions of the Prandtl number for the liquid and the Biot number for the interface, and comparisons are made with available experimental observations.

Smith, M. K.↗

Stability Analysis of Bow Shocks

We present a linear stability analysis of bow shocks created by the interaction of a spherical wind moving with respect to its surrounding medium. The bounding shocks are assumed isothermal and with Mach number M = infinity. Following Soker (1990) we study the evolution of short wavelength perturbations. We find that the motion is unstable in this limit. Moreover, the ratio of the wind velocity v(sub w) to the star velocity v(sub *) characterizes the stability properties. Bow shocks with fast winds for which v(sub *)/v(sub w)<<1 are more stable than bow sho with slow winds i.e. v(sub *)/v(sub w)>>1.

Bow Shocks↗

The dynamics and control of large flexible space structures - 13

The optimal control of three-dimensional large angle maneuvers and vibrations of a Shuttle-mast-reflector system is considered. The nonlinear equations of motion are formulated by using Lagrange's formula, with the mast modeled as a continuous beam subject to three-dimensional deformations. Pontryagin's Maximum Principle is applied to the slewing problem, to derive the necessary conditions for the optimal controls, which are bounded by given saturation levels. The resulting two point boundary value problem is then solved by using the quasilinearization algorithm and the method of particular solutions. The study of the large angle maneuvering of the Shuttle-beam-reflector spacecraft in the plane of a circular earth orbit is extended to consider the effects of the structural offset connection, the axial shortening, and the gravitational torque on the slewing motion. Finally the effect of additional design parameters (such as related to additional payload requirement) on the linear quadratic regulator based design of an orbiting control/structural system is examined.

Bainum, Peter M.↗

Low-frequency macroscopic instabilities of fully ionized magnetoplasma

Studies are described of low-frequency quasi-static instabilities in a fully ionized plasma. The plasma is assumed to be immersed in a uniform magnetic field, and is either uniform or has a number density gradient perpendicular to the magnetic field. A moment equation description of the ion and electron dynamics is used; collisions are assumed to have a strong effect on electron motion along the magnetic field. Before considering specific modes, a stability analysis is developed which allows a classification of wave growth characteristics to be made for a bounded system from solutions to the dispersion relation for an infinite system. Also, a method is given for calculating the normal mode frequencies and wave profiles by using the reflection coefficients at the boundaries. For wave propagation perpendicular to the magnetic field, the flute wave is studied in cylindrical geometry. The destabilizing effect of a radial electric field is considered by solving a differential equation.

Rognlien, T. D.↗

Binary Black Hole Mergers in the First Advanced LIGO Observing Run

The first observational run of the Advanced LIGO detectors, from September 12, 2015 to January 19, 2016, saw the first detections of gravitational waves from binary black hole mergers. In this paper we present full results from a search for binary black hole merger signals with total masses up to 100M solar mass and detailed implications from our observations of these systems. Our search, based on general-relativistic models of gravitational wave signals from binary black hole systems, unambiguously identified two signals, GW150914 and GW151226, with a significance of greater than 5 alpha over the observing period. It also identified a third possible signal, LVT151012, with substantially lower significance, which has a 87 probability of being of astrophysical origin. We provide detailed estimates of the parameters of the observed systems. Both GW150914 and GW151226 provide an unprecedented opportunity to study the two-body motion of a compact-object binary in the large velocity, highly nonlinear regime. We do not observe any deviations from general relativity, and place improved empirical bounds on several high-order post-Newtonian coefficients. From our observations we infer stellar-mass binary black hole merger rates lying in the range 9-240 Gpc-3 yr-1. These observations are beginning to inform astrophysical predictions of binary black hole formation rates, and indicate that future observing runs of the Advanced detector network will yield many more gravitational wave detections.

Abbott, B. P.↗

Maneuver simulations of flexible spacecraft by solving TPBVP

The optimal control of large angle rapid maneuvers and vibrations of a Shuttle mast reflector system is considered. The nonlinear equations of motion are formulated by using Lagrange's formula, with the mast modeled as a continuous beam. The nonlinear terms in the equations come from the coupling between the angular velocities, the modal coordinates, and the modal rates. Pontryagin's Maximum Principle is applied to the slewing problem, to derive the necessary conditions for the optimal controls, which are bounded by given saturation levels. The resulting two point boundary value problem (TPBVP) is then solved by using the quasilinearization algorithm and the method of particular solutions. In the numerical simulations, the structural parameters and the control limits from the Spacecraft Control Lab Experiment (SCOLE) are used. In the 2-D case, only the motion in the plane of an Earth orbit or the single axis slewing motion is discussed. In the 3-D slewing, the mast is modeled as a continuous beam subjected to 3-D deformations. The numerical results for both the linearized system and the nonlinear system are presented to compare the differences in their time response.

Bainum, Peter M.↗

Analysis of spinning in a monoplane wing by the induction method as compared with the strip method

The problem of autorotation has been attacked by various authors, in particular Fuchs and Schmidt who applied the so-called strip method which is based upon the assumption that the forces and moments per unit length acting in each section of the wing are equal to those on an infinite cylindrical wing of equal section in an air flow of intensity and direction resulting from the apparent relative motion of this section with respect to the surrounding air. In other words they disregarded the induced velocities, which, however, are of such importance that their omission is bound to result in appreciable errors, as we attempt to prove in this report.

Poggi, L↗

The high-latitude cloud MBM 7. I. H I and CO observations

The high-latitude cloud (HLC) MBM 7 has been observed in the 21 cm H I line and the 12CO(1-0) and 13CO(1-0) lines with similar spatial resolutions. The data reveal a total mass approximately 30 M solar for MBM 7 and a complex morphology. The cloud consists of a cold dense core of 5 M solar surrounded by atomic and molecular gas with about 25 M solar, which is embedded in hotter and more diffuse H I gas. We derive a total column density N(H I + 2H2) of 1 x 10(21) cm-2 toward the center and 1 x 10(20) cm-3 toward the envelope of MBM 7. The CO line indicates the existence of dense cores [n(H2) > or = 2000 cm-3] of size (FWHM) approximately 0.5 pc. The morphology suggests shock compression from the southwest direction, which can form molecular cores along the direction perpendicular to the H I distribution. The H I cloud extends to the northeast, and the velocity gradient appears to be about 2.8 km s-1 pc-1 in this direction, which indicates a systematic outward motion which will disrupt the cloud in approximately 10(6) yr. The observed large line widths of approximately 2 km s-1 for CO suggest that turbulent motions exist in the cloud, and hydrodynamical turbulence may dominate the line broadening. Considering the energy and pressure of MBM 7, the dense cores appear not to be bound by gravity, and the whole cloud including the dense cores seem to be expanding. The distance to HLCs suggest that they belong to the galactic plane, since the scale height of the cloud is < or approximately equal to 100 pc. Compared to the more familiar dense dark clouds, HLCs may differ only in their small mass and low density, with their proximity reducing the filling factor and enhancing the contrast of the core and envelope structure.

Non-NASA Center↗