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NASA NTRS1984

Differential rotation in a solar-driven quasi-axisymmetric circulation

The concept of a quasi-axisymmetric circulation is used to explore the global scale dynamics of planetary atmospheres. A numerical circulation model applicable to Jupiter is presented, and an analytical study is performed elucidating the conditions leading to differential rotation in an atmosphere which is convectively unstable. A linear system forced by solar differential heating is considered, with nonlinear effects arising from advection being represented in the form of eddy diffusion. An empirical, latitudinal spectrum of the observed zonal wind field on Jupiter is discussed. Numerical solutions are presented which reveal banded wind fields with alternating and equatorial zonal jets and a multicellular Ferrel-Thomson meridional circulation consistent with the observed cloud striations on Jupiter. The vertical derivatives are parameterized to construct a simplified one-layer model.

Mayr, H. G.↗

NASA NTRS1987

Viscous damped space structure for reduced jitter

A technique to provide modal vibration damping in high performance space structures was developed which uses less than one once of incompressible fluid. Up to 50 percent damping can be achieved which can reduce the settling times of the lowest structural mode by as much as 50 to 1. This concept allows the designers to reduce the weight of the structure while improving its dynamic performance. Damping by this technique is purely viscous and has been shown by test to be linear over 5 orders of input magnitude. Amplitudes as low as 0.2 microinch were demonstrated. Damping in the system is independent of stiffness and relatively insensitive to temperature.

Wilson, James F.↗

NASA NTRS1988

Longitudinal long-period dynamics of aerospace craft

Linear analyses are performed to examine the generic aspects of aerospace vehicle longitudinal long-period or trajectory modes of motion. The influence of Mach number, dynamic pressure, thrust-to-drag ratio, and propulsion system thrust laws on the longitudinal trajectory modes is presented in terms of phugoid frequency and damping and height mode stability. The results of these analyses are compared to flying qualities requirements where possible, and potential deficiencies in both the vehicle and the criteria are noted. A preliminary look at possible augmentation schemes to improve potential deficiencies is also presented. Interpretation of the practical consequences of the results is aided by typical time histories. Results indicate that propulsion system characteristics are the dominant influence on the longitudinal long-period flight dynamics of hypersonic aerospace craft. However, straightforward augmentation systems demonstrated the potential to accommodate these influences if the effects are included in the design process. These efforts may be hampered by a lack of design criteria for hypersonic aircraft.

Berry, Donald T.↗

NASA NTRS1952

Flight Investigation of a Mechanical Feel Device in an Irreversible Elevator Control System of a Large Airplane

Report presents the results of measurements of the longitudinal stability and control characteristics of a large airplane using a mechanical feel device in combination with a booster incorporated in the elevator-control system. Tests were made to investigate the feasibility of eliminating the aerodynamic control forces through use of a booster and of providing control-feel forces mechanically. The feel device consisted of a centering spring which restrained the control stick through a linkage which was changed as a function of the dynamic pressure. Provisions were made for trimming and for manual adjustment of the force gradient. The system was designed to approximate the control-force characteristics that would result with a conventional elevator control with linear hinge-moment characteristics.

Brown, B Porter↗

NASA NTRS2017

Understanding the Sun-Earth Libration Point Orbit Formation Flying Challenges For WFIRST and Starshade

In order to fly an occulter in formation with a telescope at the Sun-Earth L2 (SEL2) Libration Point, one must have a detailed understanding of the dy-namics that govern the restricted three body system. For initial purposes, a linear approximation is satisfactory, but operations will require a high-fidelity modeling tool along with strategic targeting methods in order to be successful. This paper focuses on the challenging dynamics of the transfer trajectories to achieve the relative positioning of two spacecraft to fly in formation at SEL2, in our case, the Wide-Field Infrared Survey Telescope (WFIRST) and a proposed Starshade. By modeling the formation transfers using a high fidelity tool, an accurate V approximation can be made to as-sist with the development of the subsystem design required for a WFIRST and Starshade formation flight mission.

Sun-Earth-Moon↗

NASA NTRS2014

Mean Flow Augmented Acoustics in Rocket Systems

Oscillatory motion in solid rocket motors and liquid engines has long been a subject of concern. Many rockets display violent fluctuations in pressure, velocity, and temperature originating from the complex interactions between the combustion process and gas dynamics. The customary approach to modeling acoustic waves inside a rocket chamber is to apply the classical inhomogeneous wave equation to the combustion gas. The assumption of a linear, non-dissipative wave in a quiescent fluid remains valid while the acoustic amplitudes are small and local gas velocities stay below Mach 0.2. The converging section of a rocket nozzle, where gradients in pressure, density, and velocity become large, is a notable region where this approach is not applicable. The expulsion of unsteady energy through the nozzle of a rocket is identified as the predominate source of acoustic damping for most rocket systems. An accurate model of the acoustic behavior within this region where acoustic modes are influenced by the presence of a steady mean flow is required for reliable stability predictions. Recently, an approach to address nozzle damping with mean flow effects was implemented by French [1]. This new approach extends the work originated by Sigman and Zinn [2] by solving the acoustic velocity potential equation (AVPE) formulated by perturbing the Euler equations [3]. The acoustic velocity potential (psi) describing the acoustic wave motion in the presence of an inhomogeneous steady high-speed flow is defined by, (del squared)(psi) − (lambda/c)(exp 2)(psi) − M(dot)[M(dot)(del)(del(psi))] − 2(lambda(M/c) + (M(dot)del(M))(dot)del(psi)−2(lambda)(psi)[M(dot)del(1/c)]=0 (1) with M as the Mach vector, c as the speed of sound, and lambda as the complex eigenvalue. French apply the finite volume method to solve the steady flow field within the combustion chamber and nozzle with inviscid walls. The complex eigenvalues and eigenvector are determined with the use of the ARPACK eigensolver. The present study employs the COMSOL Multphysics framework to solve the coupled eigenvalue problem using the finite element approach. The study requires one way coupling of the CFD High Mach Number Flow (HMNF) and mathematics module. The HMNF module evaluated the gas flow inside of a solid rocket motor using St. Robert's law modeling solid propellant burn rate, slip boundary conditions, and the supersonic outflow condition. Results from the HMNF model are used by the coefficient form of the mathematics module to determine the eigenvalues of the AVPE. The mathematics model is truncated at the nozzle sonic line, where a zero flux boundary condition is self-satisfying. The remaining boundaries are modeled with a zero flux boundary condition, assuming zero acoustic absorption on all surfaces. Pertinent results from these analyses are the complex valued eigenvalue and eigenvectors. Comparisons are made to the French results to evaluate the modeling approach. A comparison of the French results with that of the present analysis is displayed in figures 1 and 2, respectively. The graphic shows the first tangential eigenvector's real (a) and imaginary (b) values.

Fischbach, Sean R.↗

NASA NTRS1973

On the stabilization of decentralized control systems.

This paper considers the problem of stabilizing a linear time-variant multivariable system by using several local feedback control laws. Each local feedback control law depends only on partial system outputs. A necessary and sufficient condition for the existence of local control laws with dynamic compensation to stabilize a given system is derived. This condition is stated in terms of a new notion, called fixed modes, which is a natural generalization of the well-known concept of uncontrollable modes and unobservable modes that occur in centralized control system problems. A procedure that constructs a set of stabilizing feedback control laws is given.

Wang, S.-H.↗

NASA NTRS1977

Digital control of high performance aircraft using adaptive estimation techniques

In this paper, an adaptive signal processing algorithm is joined with gain-scheduling for controlling the dynamics of high performance aircraft. A technique is presented for a reduced-order model (the longitudinal dynamics) of a high performance STOL aircraft. The actual controller views the nonlinear behavior of the aircraft as equivalent to a randomly switching sequence of linear models taken from a preliminary piecewise-linear fit of the system nonlinearities. The adaptive nature of the estimator is necessary to select the proper sequence of linear models along the flight trajectory. Nonlinear behavior is approximated by effective switching of the linear models at random times, with durations reflecting aircraft motion in response to pilot commands.

Van Landingham, H. F.↗

NASA NTRS1984

Microprocessor based implementation of attitude and shape control of large space structures

The feasibility of off the shelf eight bit and 16 bit microprocessors to implement linear state variable feedback control laws and assessing the real time response to spacecraft dynamics is studied. The complexity of the dynamic model is described along with the appropriate software. An experimental setup of a beam, microprocessor system for implementing the control laws and the needed generalized software to implement any state variable feedback control system is included.

Reddy, A. S. S. R.↗

NASA NTRS2004

A Survey Of Earth-Moon Libration Orbits: Stationkeeping Strategies And Intra-Orbit Transfers

Cislunar space is a readily accessible region that may well develop into a prime staging area in the effort to colonize space near Earth or to colonize the Moon. While there have been statements made by various NASA programs regarding placement of resources in orbit about the Earth-Moon Lagrangian locations, there is no survey of the total cost associated with attaining and maintaining these unique orbits in an operational fashion. Transfer trajectories between these orbits required for assembly, servicing, and positioning of these resources have not been extensively investigated. These orbits are dynamically similar to those used for the Sun-Earth missions, but differences in governing gravitational ratios and perturbation sources result in unique characteristics. We implement numerical computations using high fidelity models and linear and nonlinear targeting techniques to compute the various maneuver (Delta)V and temporal costs associated with orbits about each of the Earth-Moon Lagrangian locations (L1, L2, L3, L4, and L5). From a dynamical system standpoint, we speak to the nature of these orbits and their stability. We address the cost of transfers between each pair of Lagrangian locations.

Folta, David↗

NASA NTRS2017

ICESAT GLAS Altimetry Measurements: Received Signal Dynamic Range and Saturation Correction

NASAs Ice, Cloud, and land Elevation Satellite (ICESat), which operated between 2003 and 2009, made the first satellite-based global lidar measurement of earths ice sheet elevations, sea-ice thickness, and vegetation canopy structure. The primary instrument on ICESat was the Geoscience Laser Altimeter System (GLAS), which measured the distance from the spacecraft to the earth's surface via the roundtrip travel time of individual laser pulses. GLAS utilized pulsed lasers and a direct detection receiver consisting of a silicon avalanche photodiode and a waveform digitizer. Early in the mission, the peak power of the received signal from snow and ice surfaces was found to span a wider dynamic range than anticipated, often exceeding the linear dynamic range of the GLAS 1064-nm detector assembly. The resulting saturation of the receiver distorted the recorded signal and resulted in range biases as large as approximately 50 cm for ice- and snow-covered surfaces. We developed a correction for this saturation range bias based on laboratory tests using a spare flight detector, and refined the correction by comparing GLAS elevation estimates with those derived from Global Positioning System surveys over the calibration site at the salar de Uyuni, Bolivia. Applying the saturation correction largely eliminated the range bias due to receiver saturation for affected ICESat measurements over Uyuni and significantly reduced the discrepancies at orbit crossovers located on flat regions of the Antarctic ice sheet.

Sun, Xiaoli↗

NASA NTRS2022

NASA Engineering and Safety Center Technical Bulletin No. 22-06: Treatment of Slosh Stability Margin Reductions for Human-Rated Launch Vehicles

Slosh dynamics pose a stability concern for human-rated launch vehicles during ascent. Historical perspectives on the treatment of slosh dynamics, newly developed rules of thumb, the utility of flight data, and methods for analyzing and dispositioning slosh instability risks should be considered when linear stability margins are lower than typically accepted for human-rated systems.

Fuel Slosh↗

NASA NTRS1999

Dynamical Signatures of Living Systems

One of the main challenges in modeling living systems is to distinguish a random walk of physical origin (for instance, Brownian motions) from those of biological origin and that will constitute the starting point of the proposed approach. As conjectured, the biological random walk must be nonlinear. Indeed, any stochastic Markov process can be described by linear Fokker-Planck equation (or its discretized version), only that type of process has been observed in the inanimate world. However, all such processes always converge to a stable (ergodic or periodic) state, i.e., to the states of a lower complexity and high entropy. At the same time, the evolution of living systems directed toward a higher level of complexity if complexity is associated with a number of structural variations. The simplest way to mimic such a tendency is to incorporate a nonlinearity into the random walk; then the probability evolution will attain the features of diffusion equation: the formation and dissipation of shock waves initiated by small shallow wave disturbances. As a result, the evolution never "dies:" it produces new different configurations which are accompanied by an increase or decrease of entropy (the decrease takes place during formation of shock waves, the increase-during their dissipation). In other words, the evolution can be directed "against the second law of thermodynamics" by forming patterns outside of equilibrium in the probability space. Due to that, a specie is not locked up in a certain pattern of behavior: it still can perform a variety of motions, and only the statistics of these motions is constrained by this pattern. It should be emphasized that such a "twist" is based upon the concept of reflection, i.e., the existence of the self-image (adopted from psychology). The model consists of a generator of stochastic processes which represents the motor dynamics in the form of nonlinear random walks, and a simulator of the nonlinear version of the diffusion equation which represents the mental dynamics. It has been demonstrated that coupled mental-motor dynamics can simulate emerging self-organization, prey-predator games, collaboration and competition, "collective brain," etc.

Zak, M.↗

NASA NTRS2001

Advanced Aerodynamic Design of Passive Porosity Control Effectors

This paper describes aerodynamic design work aimed at developing a passive porosity control effector system for a generic tailless fighter aircraft. As part of this work, a computational design tool was developed and used to layout passive porosity effector systems for longitudinal and lateral-directional control at a low-speed, high angle of attack condition. Aerodynamic analysis was conducted using the NASA Langley computational fluid dynamics code USM3D, in conjunction with a newly formulated surface boundary condition for passive porosity. Results indicate that passive porosity effectors can provide maneuver control increments that equal and exceed those of conventional aerodynamic effectors for low-speed, high-alpha flight, with control levels that are a linear function of porous area. This work demonstrates the tremendous potential of passive porosity to yield simple control effector systems that have no external moving parts and will preserve an aircraft's fixed outer mold line.

Hunter, Craig A.↗

NASA NTRS1988

Random field estimation approach to multibody dynamics

The use of recursive techniques similar to random field models to factor and invert the inertia matrix of a multibody system is discussed. An equivalence is established between the composite multibody system inertia matrix and the covariance of the output of a described linear system model. Conditional mean estimation and sequential estimation problems are solved along with problems of filtering and smoothing. Formulas are developed to compute the covariance of several relevant quantities. The foregoing results are used to obtain the inverse of the composite multibody system inertia in closed form.

Rodriguez, G.↗

NASA NTRS1994

Magnetotail dynamics under isobaric constraints

Using linear theory and nonlinear MHD simulations, we investigate the resistive and ideal MHD stability of two-dimensional plasma configurations under the isobaric constraint dP/dt = 0, which in ideal MHD is equivalent to conserving the pressure function P = P(A), where A denotes the magnetic flux. This constraint is satisfied for incompressible modes, such as Alfven waves, and for systems undergoing energy losses. The linear stability analysis leads to a Schroedinger equation, which can be investigated by standard quantum mechanics procedures. We present an application to a typical stretched magnetotail configuration. For a one-dimensional sheet equilibrium characteristic properties of tearing instability are rediscovered. However, the maximum growth rate scales with the 1/7 power of the resistivity, which implies much faster growth than for the standard tearing mode (assuming that the resistivity is small). The same basic eigen-mode is found also for weakly two-dimensional equilibria, even in the ideal MHD limit. In this case the growth rate scales with the 1/4 power of the normal magnetic field. The results of the linear stability analysis are confirmed qualitatively by nonlinear dynamic MHD simulations. These results suggest the interesting possibility that substorm onset, or the thinning in the late growth phase, is caused by the release of a thermodynamic constraint without the (immediate) necessity of releasing the ideal MHD constraint. In the nonlinear regime the resistive and ideal developments differ in that the ideal mode does not lead to neutral line formation without the further release of the ideal MHD constraint; instead a thin current sheet forms. The isobaric constraint is critically discussed. Under perhaps more realistic adiabatic conditions the ideal mode appears to be stable but could be driven by external perturbations and thus generate the thin current sheet in the late growth phase, before a nonideal instability sets in.

Birn, Joachim↗

NASA NTRS2000

Adjoints and Low-rank Covariance Representation

Quantitative measures of the uncertainty of Earth System estimates can be as important as the estimates themselves. Second moments of estimation errors are described by the covariance matrix, whose direct calculation is impractical when the number of degrees of freedom of the system state is large. Ensemble and reduced-state approaches to prediction and data assimilation replace full estimation error covariance matrices by low-rank approximations. The appropriateness of such approximations depends on the spectrum of the full error covariance matrix, whose calculation is also often impractical. Here we examine the situation where the error covariance is a linear transformation of a forcing error covariance. We use operator norms and adjoints to relate the appropriateness of low-rank representations to the conditioning of this transformation. The analysis is used to investigate low-rank representations of the steady-state response to random forcing of an idealized discrete-time dynamical system.

Tippett, Michael K.↗

NASA NTRS1972

Biased estimation for dynamic systems.

Optimization and regulation of static and dynamic systems require good estimates of the states of the system model and the parameters of the model in the presence of input and measurement noise. A biased estimator is proposed as an alternative to the familiar best linear unbiased estimator. Depending on the value of a constant, this biased estimator can be made unbiased and is then identical to the best linear unbiased estimator, thus permitting additional freedom of choice in design and application. The sum of squared errors of this bs tmator can be less than the best linear unbiased case. An existence theorem is established and various properties are discussed.

Chang, J. W.↗