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Results for “linear stability analysis”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
NASA NTRS1973

Stability analysis and trend study of a balloon tethered in a wind, with experimental comparisons

A stability analysis and trend study for a balloon tethered in a steady wind are presented. The linearized, stability-derivative type analysis includes balloon aerodynamics, buoyancy, mass (including apparent mass), and static forces resulting from the tether cable. The analysis has been applied to a balloon 7.64 m in length, and the results are compared with those from tow tests of this balloon. This comparison shows that the analysis gives reasonable predictions for the damping, frequencies, modes of motion, and stability boundaries exhibited by the balloon. A trend study for the 7.64-m balloon was made to illustrate how the stability boundaries are affected by changes in individual stability parameters. The trends indicated in this study may also be applicable to many other tethered-balloon systems.

Redd, L. T.↗
NASA NTRS1980

Longitudinal stability and control in wind shear with energy height rate feedback

The longitudinal linearized equations of motion in wind shear were derived for the NASA Terminal Configured Vehicle, a modified Boeing 737 airplane. In addition to the apparent acceleration terms resulting from wind shear, the equations included altitude dependent stability derivatives. A linear analysis of these equations indicates a first order divergence type of instability due to wind shear in which head wind decreased with altitude. Furthermore, this instability cannot be stabilized by attitude control alone. However, attitude control used in combination with an addition feedback loop which consisted of the energy height rate feedback to the throttle proved to be effective in suppressing instability due to wind shear. A brief piloted, real time, nonlinear simulation indicated the desirability of using a display based on the rate of change of energy height rate and of commanded thrust.

Gera, J.↗
DOE OSTI2023

Uniform-density Bose-Einstein condensates of the Gross-Pitaevskii equation found by solving the inverse problem for the confining potential

Here, in this work, we consider a “reverse-engineering” approach to construct confining potentials that support exact, constant density kovaton solutions to the classical Gross-Pitaevskii equation (GPE) also known as the nonlinear Schr¨odinger equation (NLSE). In the one-dimensional case, the exact solution is the sum of stationary kink and anti-kink solutions, i.e. a kovaton, and in the overlapping region, the density is constant. In higher dimensions, the exact solutions are generalizations of this wave function. In the absence of self-interactions, the confining potential is similar to a smoothed out finite square well with minima also at the edges. When self-interactions are added, a term proportional to ±gψ*ψ gets added to the confining potential and ±gM, where M is the norm, gets added to the total energy. In the realm of stability analysis, we find (linearly) stable solutions in the case with repulsive self-interactions which also are stable to self-similar deformations. For attractive interactions, however, the minima at the edges of the potential get deeper and a barrier in the center forms as we increase the norm. This leads to instabilities at a critical value of M (related to the number of particles in the BEC). Comparing the stability criteria from Derrick’s theorem and Bogoliubov-de Gennes analysis stability results, we find that both predict stability for repulsive self-interactions and instability at a critical mass M for attractive interactions. However, the numerical analysis gives a much lower critical mass. The numerical analysis shows further that the initial instabilities violate the symmetry x → -x assumed by Derrick’s theorem.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

The arbitrary‐order virtual element method for linear elastodynamics models: convergence, stability and dispersion‐dissipation analysis

Abstract We design the conforming virtual element method for the numerical approximation of the two‐dimensional elastodynamics problem. We prove stability and convergence of the semidiscrete approximation and derive optimal error estimates under h ‐ and p ‐refinement in both the energy and the L 2 norms. The performance of the proposed virtual element method is assessed on a set of different computational meshes, including nonconvex cells up to order four in the h ‐refinement setting. Exponential convergence is also experimentally observed under p ‐refinement. Finally, we present a dispersion‐dissipation analysis for both the semidiscrete and fully discrete schemes, showing that polygonal meshes behave as classical simplicial/quadrilateral grids in terms of dispersion‐dissipation properties.

Antonietti, Paola F.↗
NASA NTRS1976

High angle-of-attack stability-and-control analysis

Methods of linear systems analysis were applied to mathematical models of aircraft flying at high angle of attack and maneuver rate. First order longitudinal and lateral directional coupling is obtained by linearizing the complete nonlinear equations of motion about a generalized (quasi steady) trim point. Open loop stability boundaries are defined using the linear dynamic equations, and pilot in the loop effects are presented. Stability augmentation structures for maneuvering flight conditions are shown to be defined readily using optimal control theory.

Stengel, R. F.↗
NASA NTRS1982

Stability of mean flows over an infinite flat plate

The present investigation is mainly concerned with a stability analysis for the linearized Navier-Stokes equations for parallel and nonparallel mean flows over an infinite flat plate. The system of equations for parallel flows is presented. The system is viewed as a generalized Orr-Sommerfeld equation. Attention is given to an explicit criterion characterizing the case when the stability of all physically reasonable solutions is determined by the eigenvalues. The proof given in the investigation is applicable to both the generalized Orr-Somerfeld equations and the modified equations for nonparallel flow. The fact that the criterion is independent of the completeness or incompleteness of eigenfunctions is contrary to some expectations.

Miklavcic, M.↗
NASA NTRS1979

Nonparallel stability of two-dimensional nonuniformly heated boundary-layer flows

An analysis is presented for the linear stability of water boundary-layer flows over nonuniformly flat plates. Included in the analysis are disturbances due to velocity, pressure, temperatures, density, and transport properties as well as variations of the liquid properties with temperature. The method of multiple scales is used to account for the nonparallelism of the mean flow. In contrast with previous analyses, the nonsimilarity of the mean flow is taken into account. No analysis agrees, even qualitatively, with the experimental data when similar profiles are used. However, both the parallel and nonparallel results qualitatively agree with the experimental results of Strazisar and Reshotko when nonsimilar profiles are used.

Nayfeh, A. H.↗
NASA NTRS1976

Linearized blade row compression component model. Stability and frequency response analysis of a J85-3 compressor

NASA developed stability and frequency response analysis techniques were applied to a dynamic blade row compression component stability model to provide a more economic approach to surge line and frequency response determination than that provided by time-dependent methods. This blade row model was linearized and the Jacobian matrix was formed. The clean-inlet-flow stability characteristics of the compressors of two J85-13 engines were predicted by applying the alternate Routh-Hurwitz stability criterion to the Jacobian matrix. The predicted surge line agreed with the clean-inlet-flow surge line predicted by the time-dependent method to a high degree except for one engine at 94% corrected speed. No satisfactory explanation of this discrepancy was found. The frequency response of the linearized system was determined by evaluating its Laplace transfer function. The results of the linearized-frequency-response analysis agree with the time-dependent results when the time-dependent inlet total-pressure and exit-flow function amplitude boundary conditions are less than 1 percent and 3 percent, respectively. The stability analysis technique was extended to a two-sector parallel compressor model with and without interstage crossflow and predictions were carried out for total-pressure distortion extents of 180 deg, 90 deg, 60 deg, and 30 deg.

Tesch, W. A.↗
NASA NTRS1986

Control design for robust stability in linear regulators: Application to aerospace flight control

Time domain stability robustness analysis and design for linear multivariable uncertain systems with bounded uncertainties is the central theme of the research. After reviewing the recently developed upper bounds on the linear elemental (structured), time varying perturbation of an asymptotically stable linear time invariant regulator, it is shown that it is possible to further improve these bounds by employing state transformations. Then introducing a quantitative measure called the stability robustness index, a state feedback conrol design algorithm is presented for a general linear regulator problem and then specialized to the case of modal systems as well as matched systems. The extension of the algorithm to stochastic systems with Kalman filter as the state estimator is presented. Finally an algorithm for robust dynamic compensator design is presented using Parameter Optimization (PO) procedure. Applications in a aircraft control and flexible structure control are presented along with a comparison with other existing methods.

Yedavalli, R. K.↗
NASA NTRS1984

Investigation of dynamic noise affecting geodynamics information in a tethered subsatellite

The effects of a tethered satellite system's internal dynamics on the subsatellite were calculated including both overall motions (libration and attitude oscillations) and internal tether oscillations. The SKYHOOK tether simulation program was modified to operate with atmospheric density variations and to output quantities of interest. Techniques and software for analyzing the results were developed including noise spectral analysis. A program was begun for computing a stable configuration of a tether system subject to air drag. These configurations will be of use as initial conditions for SKYHOOK and, through linearized analysis, directly for stability and dynamical studies. A case study in which the subsatellite traverses an atmospheric density enhancement confirmed some theoretical calculations, and pointed out some aspects of the interaction with the tether system dynamics.

Gullahorn, G. E.↗
NASA NTRS1984

The dynamic fission instability and the origin of the Moon

A theory for the formation of the Moon which involves the dynamic fission of a rapidly rotating protoplanet, which might then result in the formation of the Earth and the Moon is discussed. The fission hypothesis was originally based on analytic, linearized models of the growth of asymmetry in homogenous bodies. The fully nonlinear evolution of the dynamic instability in inviscid, compressible bodies was calculated by numerical techniques. It was found that the dynamic instability degenerates into the ejection of a ring of matter with a substantial fraction of the mass, leaving behind a central body with most of the mass. The linearized analytical approach and the numerical approach were used to show that dynamic fission probably does not occur in rocky protoplanets. The numerical calculations are performed with a fully three dimensional hydrodynamical code, which allows the nonlinear, time evolution of the instability to be followed. Sequences of uniformly rotating equilibria were constructed and are used as the initial models for the fission calculations. An initially imposed asymmetry consisting of a 10% binary perturbation in the density was found to disappear on the rotational period time scale. No dynamic instability occurred. This result are verified by including the velocity dissipation terms in the linearized analysis of the stability of a Maclaurin spheroid: the dynamic instability disappears when the simulated viscous dissipation terms are included. It is concluded that any rocky body, even with considerable partial melt or a molten core, should be stable to dynamic fission; any rotational instability that occurs can only result in equatorial mass loss.

Boss, A. P.↗
NASA NTRS1992

Radiative instabilities and 1000 second fluctuations in astrophysical masers

A stability analysis for small (linear) perturbations is presented for the radiation in astrophysical masers treated in the usual, linear maser approximation. Instabilities that oscillate with a period of about L/c, where L is the length of the maser are found. They occur (1) when the maser is partly but not heavily saturated, (2) when the decay rate Gamma for the molecular states is near c/L, and (3) when the product of the brightness temperature T sub 0 of the incident radiation and the angle for the beaming is less than a critical value that depends upon the particular masing transition. A fourth parameter, the fractional inversion in the pumping multiplied by (T sub 0/frequency), determines the importance of spontaneous emission which can eliminate the instabilities. These instabilities are a likely cause for the fluctuations in the radiation from the 18 cm OH masers that have been reported to occur on time scales as short as 1000 s. The calculations are applicable to other types of astrophysical masers as well, and suggest that spontaneous emission will prevent similar instabilities in the H2O and SiO masers.

Scappaticci, Gerardo A.↗
NASA NTRS1993

The effect of gravitational modulation on convection in vertical Bridgman growth

During vertical directional solidification of a binary alloy at constant velocity, buoyancy-driven solutal convection may occur due to the solute gradient associated with the solidification process. This problem is further complicated if time-periodic forcing is considered, which is relevant to materials processing in a microgravity environment or as a means of dynamic control of flow instabilities. The effect of time-periodic modulation is studied by introducing a gravitational acceleration which is a sinusoidal function of time. The onset of solutal convection is treated by a stability analysis of the linearized governing equations and boundary conditions. Solutions are obtained numerically employing two distinct computational implementations of Floquet theory. Results are presented for materials with large Schmidt number, and an analysis for large frequency and large Schmidt number yields a more complete description of the behavior in this relevant limit.

Murray, B. T.↗
NASA NTRS1993

A hydrodynamical model for the explosion of a neutron star just below the minimum mass

The instability of a neutron star at the minimum mass is investigated using a hydrodynamical model to follow the evolution of the unstable star. A detailed analysis of the linear stability of the equilibrium configurations near the minimum mass is performed by solving the radial eigenvalue problem for the fundamental mode. The minimum mass configuration M(mmc) of 0.196 solar mass is found to be stable to small perturbations. Stability to radial perturbations is lost only at a lower critical mass of 0.16 solar mass, corresponding to about 0.8 M(mmc). It is shown that a simple dynamical model constructed using a 3-polytrope equation of state for hot dense matter reproduces the key dynamical features of the instability in the explosion phase.

Colpi, Monica↗
NASA NTRS1992

The effect of gravitational modulation on convection in vertical Bridgman growth

During vertical directional solidification of a binary alloy at constant velocity, buoyancy driven solutal convection may occur due to the solute gradient associated with the solidification process. This problem is further complicated if time periodic forcing is considered, which is relevant to materials processing in a microgravity environment or as a means of dynamic control of flow instabilities. The effect of time periodic modulation is studied by introducing a gravitational acceleration which is a sinusoidal function of time. The onset of solutal convection is treated by a stability analysis of the linearized governing equations and boundary conditions. Solutions are obtained numerically by employing two distinct computational implementations of Floquet theory. Results for materials with large Schmidt number are presented, and an analysis for large frequency and large Schmidt number yields a more complete description of the behavior in this relevant limit.

Murray, Bruce T.↗
NASA NTRS2005

The Use of a Gyroless Wheel-Tach Controller in SDO Safehold Mode

This paper describes the progression of the Safehold mode design on the Solar Dynamics Observatory satellite. Safehold uses coarse Sun sensors and reaction wheel tachometers to keep the spacecraft in a thermally safe and power-positive attitude. The control algorithm is described, and simulation results shown. Specific control issues arose when the spacecraft entered eclipse, and a description of the trade study which added gyroscopes to the mode is included. The paper concludes with the results from the linear and nonlinear stability analysis.

Bourkland, Kristin L.↗
NASA NTRS2011

Linear Approximation to Optimal Control Allocation for Rocket Nozzles with Elliptical Constraints

In this paper we present a straightforward technique for assessing and realizing the maximum control moment effectiveness for a launch vehicle with multiple constrained rocket nozzles, where elliptical deflection limits in gimbal axes are expressed as an ensemble of independent quadratic constraints. A direct method of determining an approximating ellipsoid that inscribes the set of attainable angular accelerations is derived. In the case of a parameterized linear generalized inverse, the geometry of the attainable set is computationally expensive to obtain but can be approximated to a high degree of accuracy with the proposed method. A linear inverse can then be optimized to maximize the volume of the true attainable set by maximizing the volume of the approximating ellipsoid. The use of a linear inverse does not preclude the use of linear methods for stability analysis and control design, preferred in practice for assessing the stability characteristics of the inertial and servoelastic coupling appearing in large boosters. The present techniques are demonstrated via application to the control allocation scheme for a concept heavy-lift launch vehicle.

Orr, Jeb S.↗