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At least 199 records · Page 11

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↗

Trajectory Control of Rendezvous with Maneuver Target Spacecraft

In this paper, a nonlinear trajectory control algorithm of rendezvous with maneuvering target spacecraft is presented. The disturbance forces on the chaser and target spacecraft and the thrust forces on the chaser spacecraft are considered in the analysis. The control algorithm developed in this paper uses the relative distance and relative velocity between the target and chaser spacecraft as the inputs. A general formula of reference relative trajectory of the chaser spacecraft to the target spacecraft is developed and applied to four different proximity maneuvers, which are in-track circling, cross-track circling, in-track spiral rendezvous and cross-track spiral rendezvous. The closed-loop differential equations of the proximity relative motion with the control algorithm are derived. It is proven in the paper that the tracking errors between the commanded relative trajectory and the actual relative trajectory are bounded within a constant region determined by the control gains. The prediction of the tracking errors is obtained. Design examples are provided to show the implementation of the control algorithm. The simulation results show that the actual relative trajectory tracks the commanded relative trajectory tightly. The predicted tracking errors match those calculated in the simulation results. The control algorithm developed in this paper can also be applied to interception of maneuver target spacecraft and relative trajectory control of spacecraft formation flying.

Zhou, Zhinqiang↗

Spectral distortions to momentum and scalar exchanges by non-turbulent motion and patchy landscape variability

Modifications to the spectra of turbulent velocity and scalars and co-spectra of vertical fluxes of momentum and scalars due to patchy landscape heterogeneity and non-stationarity are explored for a Mediterranean ecosystem. About 9 months of high frequency measurements of the three velocity components, water vapor concentration, carbon dioxide concentration, and air temperature were analyzed for different seasons (spring/summer) and prevalent wind directions (southeast/northwest). The two wind directions sampled a contrast of clumped and patchy landscape comprised of olive trees (southeast) and wall bounded flow disturbed by the presence of few upwind trees (northwest). The measured spectra and co-spectra were also compared to theoretical scaling forms from stationary, planar homogeneous flow, in the absence of subsidence as derived from the Kansas experiment. To assess the role of low frequency non-turbulent motion on the spectral and co-spectral content, a 5-min Fourier cutoff was introduced and the analysis was limited to near-neutral conditions where the boundary layer depth is shallow compared to its unstable counterpart. It was shown that the velocity statistics were not appreciably impacted by the low-frequency motion causing non-stationarity. Moreover, the turbulent scalar fluxes were also shown not to be significantly impacted by such low frequency motion. The scalar variances were impacted, especially the water vapor variance and its concomitant spectral shape. When the non-turbulent motion was filtered, the scalar spectra at low wavenumbers followed expectations from the so-called attached eddy hypothesis (i.e. exhibited a $k^{-1}_x$ scaling with $k_x$ defining the longitudinal wavenumber) applicable for near-neutral conditions. For momentum co-spectra, the canonical shapes from the Kansas experiment appear to describe well the measurements here and in both dominant directions and seasons with some adjustment to the integral time scales based on wind direction. For the scalar co-spectra, deviations from the Kansas experiment were prevalent. The most noticeable and surprising deviations were their slow decay with increased sampling frequency at inertial subrange scales. This slow decay was shown not to contribute appreciably to the overall scalar fluxes. At those fine scales, predictions from local isotropy were expected to hold. The scalar co-spectral deviations from local isotropy were then discussed using a simplified co-spectral budget model where scalar–scalar co-spectra naturally emerged and the interplay between landscape heterogeneity and a scale-dependent pressure-scalar de-correlation time was postulated. It is also envisaged that the findings here offer a preliminary template for analyzing eddy-covariance data in situations that deviate from ideal conditions, especially regarding low-frequency modulations of scalar spectra and vertical scalar flux co-spectra.

Canopy turbulence↗

Harmonic oscillator representation in the theory of scattering and nuclear reactions

The following questions, concerning the application of the harmonic oscillator representation (HOR) in the theory of scattering and reactions, are discussed: the formulation of the scattering theory in HOR; exact solutions of the free motion Schroedinger equation in HOR; separable expansion of the short range potentials and the calculation of the phase shifts; 'isolated states' as generalization of the Wigner-von Neumann bound states embedded in continuum; a nuclear coupled channel problem in HOR; and the description of true three body scattering in HOR. As an illustration the soft dipole mode in the (11)Li nucleus is considered in a frame of the (9)Li+n+n cluster model taking into account of three body continuum effects.

Smirnov, Yuri F.↗

Don't cross the streams: caustics from fuzzy dark matter

Here we study how tidal streams from globular clusters may be used to constrain the mass of ultra-light dark matter particles, called `fuzzy' dark matter (FDM). A general feature of FDM models is the presence of ubiquitous density fluctuations in bound, virialized dark matter structures, on the scale of the de Broglie wavelength, arising from wave interference in the evolving dark matter distribution. These time-varying fluctuations can disturb the motions of stars, leading to potentially observable signatures in cold thin tidal streams in our own Galaxy. The study of this effect has been hindered by the difficulty in simulating the FDM wavefunction in Milky Way-sized systems. We present a simple method to evolve realistic wavefunctions in nearly static potentials, that should provide an accurate estimate of this granulation effect. We quantify the impact of FDM perturbations on tidal streams, and show that initially, while stream perturbations are small in amplitude, their power spectra exhibit a sharp cutoff corresponding to the de Broglie wavelength of the FDM potential fluctuations. Eventually, when stream perturbations become nonlinear, fold caustics generically arise that lead to density fluctuations with universal behavior. This erases the signature of the de Broglie wavelength in the stream density power spectrum, but we show that it will still be possible to determine the FDM mass in this regime, by considering the fluctuations in quantities like angular momenta or actions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Nonlinear causality of Israel-Stewart theory with diffusion

We present the first fully nonlinear causality constraints in D = 3 + 1 dimensions for Israel-Stewart theory in the presence of energy and number diffusion in the Eckart and Landau hydrodynamic frames, respectively. These constraints are algebraic inequalities that make no assumption on the underlying geometry of the spacetime or the equation of state. In order to highlight the distinct physical and structural behavior of the two hydrodynamic frames, we discuss the special ultrarelativistic ideal gas equation of state considered in earlier literature in D = 1 + 1 dimensions, and show that our general D = 3 + 1 constraints reduce to their results upon an appropriate choice of angles. For this equation of state in both D = 1 + 1 and D = 3 + 1 dimensions one can show that: (i) there exists a region allowed by nonlinear causality in which the baryon current transitions into a spacelike vector in the Landau frame, and (ii) an analogous argument shows that the solutions of the Eckart frame equations of motion never violate the dominant energy condition, assuming nonlinear causality holds. Furthermore, we then compare our results with those from linearized Israel-Stewart theory and show that the linear causality bounds fail to capture the new physical constraints on energy and number diffusion that are successfully obtained through our nonlinear causality approach.

Quark-gluon plasma↗

Acoustoelasticity

Sound or pressure variations inside bounded enclosures are investigated. Mathematical models are given for determining: (1) the interaction between the sound pressure field and the flexible wall of a Helmholtz resonator; (2) coupled fluid-structural motion of an acoustic cavity with a flexible and/or absorbing wall; (3) acoustic natural modes in multiple connected cavities; and (4) the forced response of a cavity with a flexible and/or absorbing wall. Numerical results are discussed.

Dowell, E. H.↗

Gain-Scheduled Fault Tolerance Control Under False Identification

An active fault tolerant control (FTC) law is generally sensitive to false identification since the control gain is reconfigured for fault occurrence. In the conventional FTC law design procedure, dynamic variations due to false identification are not considered. In this paper, an FTC synthesis method is developed in order to consider possible variations of closed-loop dynamics under false identification into the control design procedure. An active FTC synthesis problem is formulated into an LMI optimization problem to minimize the upper bound of the induced-L2 norm which can represent the worst-case performance degradation due to false identification. The developed synthesis method is applied for control of the longitudinal motions of FASER (Free-flying Airplane for Subscale Experimental Research). The designed FTC law of the airplane is simulated for pitch angle command tracking under a false identification case.

Shin, Jong-Yeob↗

Development of a Test Facility for Air Revitalization Technology Evaluation

An active fault tolerant control (FTC) law is generally sensitive to false identification since the control gain is reconfigured for fault occurrence. In the conventional FTC law design procedure, dynamic variations due to false identification are not considered. In this paper, an FTC synthesis method is developed in order to consider possible variations of closed-loop dynamics under false identification into the control design procedure. An active FTC synthesis problem is formulated into an LMI optimization problem to minimize the upper bound of the induced-L2 norm which can represent the worst-case performance degradation due to false identification. The developed synthesis method is applied for control of the longitudinal motions of FASER (Free-flying Airplane for Subscale Experimental Research). The designed FTC law of the airplane is simulated for pitch angle command tracking under a false identification case.

Lu, Sao-Dung↗

Quantum stresses in the hydrogen atom

Gravitational form factors are often interpreted as providing access to stresses inside hadrons, in particular through Fourier transforms of the form factors 𝐷 and $\bar{𝑐}$. Some researchers, however, have expressed skepticism of this interpretation. I revisit the question, and argue that it is indeed appropriate to interpret these quantities as stress distributions. I consider the hydrogen atom’s ground state as a familiar example, and use the pilot wave interpretation of quantum mechanics to give the distributions a clear meaning. A striking result is that $\bar{𝑐}$—rather than 𝐷—quantifies the force law binding the system, which can be understood through Cauchy’s first law of motion.

74 ATOMIC AND MOLECULAR PHYSICS↗

Sloshing dynamics on rotating helium dewar tank

The generalized mathematical formulation of sloshing dynamics for partially filled liquid of cryogenic superfluid helium II in dewar containers driven by both the gravity gradient and jitter accelerations applicable to scientific spacecraft which is eligible to carry out spinning motion and/or slew motion for the purpose to perform scientific observation during the normal spacecraft operation are investigated. An example is given with Gravity Probe-B (GP-B) spacecraft 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 were 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 were derived. Results were widely published in the open journals.

Hung, R. J.↗

Mountain-Top-to-Mountain-Top Optical Link Demonstration

A mountain-top-to-mountain-top optical communications demonstration was conducted between the JPL Table Mountain Facility (TMF), Wrightwood, California, and Strawberry Peak (SP), Lake Arrowhead, California, during the months of August and September of 2000. The link was nearly horizontal at an altitude of 2 km and spanned a range of 46.8 km. A 780-nm multibeam beacon broadcast from TMF was received by the JPL Optical Communications Demonstrator (OCD) located at SP. The received beacon was utilized as a pointing reference to retransmit an 852-nm communications laser beam, modulated at 400 Mb/s by a PN7 pseudo-random bit stream (PRBS) sequence. The long atmospheric path resulted in atmospheric-turbulence-induced angle-of-arrival fluctuations of the beacon at the OCD aperture. A .ne-steering control loop was used to track the resulting beacon centroid motion and update the pointing of the communications laser beam transmitted from SP to TMF. Fried parameters, or r0, inferred from focal spot sizes received at SP were 4 to 5 cm whereas, using the spot sizes received at TMF, they were 2 to 3 cm. In both cases, theory predicts larger r0 values. The predicted angle-of-arrival fluctuations compare well with measured rms displacements exhibited by the focal spots at either end of the link. An uncompensated error of ~1.1 rad in the x-axis and ~2 rad in the y-axis was obtained using centroid data logged by the OCD. Average bit-error rates of 10-5 were recorded for extended periods of time. An atmospheric coherence length r0 of 3 to 5 cm was inferred using the focal-plane spot size measured on the CCD tracking sensor and compared to a predicted value of 5 to 7 cm using reasonable atmospheric models. The irradiance bounds required for the CCD tracking sensor to perform centroiding was found to range from 2000 to 3000 integrated pixel counts, although a more reliable range was 600 to 3000, indicating a dynamic range of 6 to 11 dB. The motion of the spot on the focal plane was also recorded and yielded rms angle-of-arrival-induced focal-plane displacement of 9 to 11 m, compared to a predicted value of 7.8 to 11 m. The irradiance measurements made with the OCD clearly indicate that best tracking performance is obtained when the mean received signal is 2000 to 2200 counts. The best tracking performance resulted in an rms uncompensated error of 1.1 rad. The uncompensated error appeared to increase with either an increase or decrease in mean beacon-signal level. The rms uncompensated error determined by deriving the beacon displacement power spectral density from the beacon centroid-versustime data and the rejection function of the control loop yielded a higher value of 3.4 rad.

Biswas, A.↗

Canonical Transformation of Potential Model Hamiltonian Mechanics to Geometrical Form I

Using the methods of symplectic geometry, we establish the existence of a canonical transformation from potential model Hamiltonians of standard form in a Euclidean space to an equivalent geometrical form on a manifold, where the corresponding motions are along geodesic curves. The advantage of this representation is that it admits the computation of geodesic deviation as a test for local stability, shown in recent previous studies to be a very effective criterion for the stability of the orbits generated by the potential model Hamiltonian. We describe here an algorithm for finding the generating function for the canonical transformation and describe some of the properties of this mapping under local diffeomorphisms. We give a convergence proof for this algorithm for the one-dimensional case, and provide a precise geometric formulation of geodesic deviation which relates the stability of the motion in the geometric form to that of the Hamiltonian standard form. We apply our methods to a simple one-dimensional harmonic oscillator and conclude with a discussion of the relation of bounded domains in the two representations for which Morse theory would be applicable.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Scanning thermal plumes

Over a three-year period 800 thermal line scans of power plant plumes were made by an airborne scanner, with ground truth measured concurrently at the plants. Computations using centered finite differences in the thermal scanning imagery show a lower bound in the horizontal temperature gradient in excess of 1.6 C/m. Gradients persist to 3 m below the surface. Vector plots of the velocity of thermal fronts are constructed by tracing the front motion in successive thermal images. A procedure is outlined for the two-point ground calibration of a thermal scanner from an equation describing the scanner signal and the voltage for two known temperatures. The modulation transfer function is then calculated by input of a thermal step function and application of digital time analysis techniques using Fast Fourier Transforms to the voltage output. Field calibration tests are discussed. Data accuracy is limited by the level of ground truth effort chosen.

Scarpace, F. L.↗

Time-dependent model of the Martian atmosphere for use in orbit lifetime and sustenance studies

A time-dependent model of the Martian atmosphere suitable for calculation of long-term aerodynamic effects on low altitude satellites is presented. The atmospheric model is both position dependent, through latitude and longitude effects, and time dependent. The time dependency includes diurnal and seasonal effects, effects of annual motion, long and short term solar activity effects, and periodic dust storm effects. Nine constituent gases are included in the model. Uncertainties in exospheric temperature, turbidity, and turbopause altitude are used to produce bounds on the expected density. A computer model - a Fortran subroutine which, when given the Julian date, Cartesian position of the sun and the spacecraft in aerocentric coordinates, returns the local values of mass density, temperature, scale height, and upper and lower bounds on the mass density is presented.

Culp, R. D.↗