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All sourcesNASA NTRSDOE OSTI
NASA NTRS1975

Stability criteria for two-variable polynomials

Recursive algebraic algorithms are developed for testing various stability properties of two-variable polynomials in finite number of steps. Stability is tested with respect to either the half plane or the unit circle applying the equivalent of the Routh or Marden test only two times, regardless of the degree of the polynomial.

Siljak, D. D.↗
NASA NTRS1975

Stability criteria for two-variable polynomials

Recursive algebraic algorithms are developed for testing various stability properties of two-variable polynomials in a finite number of steps. Stability is tested with respect to either the half-plane or the unit circle applying only two times the equivalent of the Routh or Marden test, regardless of the degree of the polynomial.

Siljak, D. D.↗
NASA NTRS1971

Frequency domain stability criteria for distributed nonlinear sampled-data systems.

Popov-type sufficient conditions are presented for the absolute stability of a class of closed loop sampled-data systems. The closed loop system consists of a linear distributed element, a feedback controller (linear or nonlinear), a sampler, and possibly a zero-order hold circuit. The distributed element is assumed to be finite Hankel transformable, and such that its dynamics can be represented by a transfer function which is the ratio of the multiple (Laplace and finite Hankel) transforms of output and input. The input is assumed to be distributed. The stability criterion presented here parallels the criterion for distributed systems that are finite Fourier transformable. An example is given to illustrate the applications of the stability criterion.

Nagarajan, N.↗
NASA NTRS1989

Teleoperator comfort and psychometric stability: Criteria for limiting master-controller forces of operation and feedback during telemanipulation

The following question is addressed: How much force should operators exert, or experience, when operating a telemanipulator master-controller for sustained periods without encountering significant fatigue and discomfort, and without loss of stability in psychometric perception of force. The need to minimize exertion demands to avoid fatigue is diametrically opposed by the need to present a wide range of force stimuli to enhance perception of applied or reflected forces. For 104 minutes subjects repetitiously performed a series of 15 s isometric pinch grasps; controlled at 5, 15, and 25 percent of their maximum voluntary strength. Cyclic pinch grasps were separated by rest intervals of 7.5 and 15 s. Upon completion of every 10 minute period, subjects interrupted grasping activities to gage the intensity of fatigue and discomfort in the hand and forearm using a cross-modal matching technique. A series of psychometric tests were then conducted to determine accuracy and stability in the subject's perception of force experienced. Results showed that onset of sensations of discomfort and fatigue were dependent upon the magnitude of grasp force, work/rest ratio, and progression of task. Declines in force magnitude estimation slopes, indicating a reduction in force perception sensitivity, occurred with increased grasp force when work/rest ratios were greater than 1.0. Specific recommendations for avoiding discomfort and shifts in force perception, by limiting pinch grasp force required for master-controller operation and range of force reflection or work/rest ratios, are provided.

Wiker, Steven F.↗
NASA NTRS1974

Rigid body mode pointing accuracy and stability criteria for an orbiting spacecraft

The effect of gravity gradient torque disturbances (which is an order of magnitude greater than the other torque disturbances and is sinusoidal with a frequency of two cycles per orbit) on pointing accuracy can be predicted very precisely. However, since the sensor noise such as star tracker and gyro inherent noise, is random, their effect can only be predicted statistically. The most common method used is computer simulation with appropriate sensor model and adjusting spacecraft control laws for minimum pointing error, as presented by Harris (1972). The general investigation outlined theoretically relates spacecraft controls to pointing accuracy in terms of the sensor noise power spectrum. The results are presented in graphical form.

Sandhu, G. S.↗
NASA NTRS1974

Convection in the moon - Effect of variable viscosity

This work determines criteria for stability of the lunar interior to thermal convection in the case of variable viscosity. The conditions necessary for solid convection to play an important role in the moon's revolution are determined by application of the calculated stability criteria to a variety of thermal history models. Most thermal history temperature profiles would be unstable to solid convection at the present time, if currently used estimates of the viscosity function are applicable. A possible explanation of lunar seismic data is that temperatures near the melting point of silicates exist at depths greater than 800 km. If this is the case, either the lunar interior is stable, or solid convection is occurring at a rate insufficient to cool the lunar interior substantially. If the former is true, the viscosity of lunar material is higher than that usually assumed.

Cassen, P.↗
NASA NTRS2002

Interchange Method in Compressible Magnetized Couette Flow: Magnetorotational and Magnetoconvective Instabilities

We obtain the general forms of the axisymmetric stability criteria in a magnetized compressible Couette flow using an energy variational principle, the so-called interchange or Chandrasekhar s met hod, which we applied successfully in the incompressible case. This formulation accounts for the simultaneous presence of gravity, rotation, a toroidal magnetic field, a weak axial magnetic field, entropy gradients, and density gradients in the initial equilibrium state. The power of the method lies in its simplicity which allows us to derive extremely compact and physically clear expressions for the relevant stability criteria despite the inclusion of so many physical effects. In the implementation of the method, all the applicable conservation laws are explicitly taken into account during the variations of a quantity with dimensions of energy which we call the free energy function. As in the incompressible case, the presence of an axial field invalidates the conservation laws of angular momentum and azimuthal magnetic flux and introduces instead isorotation and axial current conservation along field lines. Our results are therefore markedly different depending on whether an axial magnetic field is present, and generalize in two simple expressions all previously known, partial stability criteria for the appearance of magnetorotational instability. Furthermore, the coupling between magnetic tension and buoyancy and its influence to the dynamics of nonhomoentropic magnetized flows becomes quite clear from our results. In the limits of plane-parallel atmospheres and homoentropic flows, our formulation easily recovers the stability criteria for suppression of convective and Parker instabilities, as well as some related special cases studied over 40 years ago by Newcomb and Tserkovnikov via laborious variational techniques.

Christodoulou, Dimitris M.↗
NASA NTRS2018

Stabilized Approach Criteria: Bridging the Gap Between Theory and Practice

Approach and landing is the most common phase of flight for aviation accidents, accounting annually for approximately 65 percent of all accidents. A Flight Safety Foundation study of 16 years of runway excursions determined that 83 percent could have been avoided with a decision to go around. In other words, 54 percent of all accidents could potentially be prevented by going around. A critical industry policy designed to help prevent such accidents is the go-around policy. However, the collective industry performance of complying with go-around policies is extremely poor and only about three percent of unstable approaches result in a go-around. Improving the go-around compliance rate holds tremendous potential in reducing approach and landing accidents. There are many reasons for flight crews ignoring go-around policies related to pilot judgement and company policies. Examples are the collective industry norm to accept the noncompliance of go-around policies, management being disengaged from go-around noncompliance, and pilot fatigue and lack of situational awareness. One of the biggest factors is that pilots see current stabilized-approach criteria as too complex and restrictive for the operational environment. Following the American Airlines 1420 accident (Little Rock, 1999), where the aircraft overran the runway upon landing and crashed, the National Transportation Safety Board (NTSB) recommended that the Federal Aviation Administration (FAA) define detailed parameters for a stabilized approach, and develop detailed criteria indicating when a go-around should be performed. The experiment discussed in this presentation is the first step towards developing these go-around criteria for commercial transport aircraft.

pilot performance↗
NASA NTRS1992

Effects of g-jitter and cross-diffusion on the onset of convection in doubly diffusive systems

The effects of a modulated gravity field in doubly diffusive layers with and without cross-diffusion are studied. Attention is focused on the determination of linear stability criteria for such systems. Floquet theory is used to establish the stability criteria by a systematic analysis of the topology of the neutral curves from which stability boundaries can be constructed. Convective stability boundaries for gravity-modulated doubly cross-diffusive systems are presented for the cases of dynamically free and rigid boundaries. Two physically different forms of layer stratification are considered: (1) imposed independent gradients of two components and (2) a solute gradient induced by a fixed temperature gradient.

Terrones, Guillermo↗