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The results of an analytical investigation of the rotational dynamics of a spinning Skylab space station are presented. The passive stability of motion of a simplified model consisting of a rigid core body with two attached flexible appendages is investigated. The parameter plane stability technique is applied to the specific Skylab case to determine its transient response to external disturbances.
The parameters are established which are important to the stability of a boundary layer flow over a yawed spinning cylinder in a uniform stream. It is shown that transition occurs asymmetrically in general and this asymmetry can be important for the prediction of aerodynamic forces and moments (e.g., the Magnus effect). Instability of the steady-state boundary layer flow is determined using small disturbance theory. Although the approach is strictly valid only for the calculation of the conditions for stability in the small, experimental data indicate that in many problems, it provides a good estimate for the transition to turbulence.
An experimental study has been conducted to determine the aerodynamic characteristics of a proposed recoverable space shuttle booster vehicle. Tests were made at Mach numbers of 0.7, 1.5, and 3.5 of two configurations, one with tail panels deflected 90 deg and one with tail panels deflected 70 deg. Both configurations were found to be highly statically stable at all Mach numbers. The dynamic behavior was erratic; the models exhibited both neutral dynamic stability and dynamic instability, and the motions experienced during free flight at the subsonic Mach number were very irregular. The flow field over the models was characterized by an extensive separated flow region which largely encompassed the tail panels. The experimental drag and static stability were not well predicted by available theoretical estimates.
The field of stochastic stability is surveyed, with emphasis on the invariance theorems and their potential application to systems with randomly varying coefficients. Some of the basic ideas are reviewed, which underlie the stochastic Liapunov function approach to stochastic stability. The invariance theorems are discussed in detail.
A small angle stability analysis is presented for one particular configuration of a high power communication satellite having a linear control system. Both the central body and the solar array are treated as rigid bodies. The control system studied consists of three-axis control of the central body and one-axis control of the solar array rotation relative to the central body. The results yield preliminary indications of the relation of stability to satellite inertias and control gains.
The stability of hingeless rotor blade oscillations in hover is examined theoretically using a simplified centrally-hinged, spring-restrained, rigid blade to approximate the deflections of actual elastic blades. The aerodynamic and inertial coupling between the flap and lead-lag degrees of freedom is primarily responsible for instability, however elastic coupling and kinematic pitch-lag coupling both exert a powerful influence on hingeless rotor blade stability. Experimental results obtained from a two-bladed 1.81m diameter model rotor designed for minimum elastic coupling have confirmed the results of linear theory. For this model configuration rotor blade stall at high pitch angles was found to counteract the destabilizing flap-lag coupling and increase the damping of lead-lag oscillations. It was possible to account for this effect with the theory by using drag data for stalled airfoils.
The changes in thrust minus drag performance as well as longitudinal and directional stability and control characteristics of a single-engine jet aircraft attributable to an in-flight thrust reverser of the blocker-deflector door type were investigated in a 16-foot transonic wind tunnel. The longitudinal and directional stability data are presented. Test conditions simulated landing approach conditions as well as high speed maneuvering such as may be required for combat or steep descent from high altitude.
The steady motion in sunspot magnetic regions is considered for both current-free and force-free configurations. The sufficient condition for stability is obtained in the presence of both external current-free and force-free magnetic fields and a steady motion. It is shown that the pattern of such steady motion is most important in triggering an instability of sunspot magnetic fields, both for the current-free and force-free configuration. When there is no steady motion, the current-free configuration of sunspot magnetic fields is always stable, whereas the stability in the case of force-free magnetic fields is connected with the configuration. The onset of a solar flare seems to be associated with an instability connected to the steady motion within the sunspot magnetic regions.
Description of some recent extensions of the invariance principle to more generalized dynamical systems where the state space is not locally compact and the flow is unique only in the forward direction of time. A sufficient condition for asymptotic stability of an invariant set is obtained which does not require that the Liapunov function be positive-definite. A recently developed generalized invariance principle is described which is applicable to functional differential equations, partial differential equations, and, in particular, to certain stability problems arising in thermoelasticity, viscoelasticity, and distributed nonlinear networks.
A linear analysis of hydrodynamic stability has been applied to a problem in which a fluid mixture is contained between two horizontal planes. One species diffuses to the lower plane where it is destroyed by a rapid exothermic or endothermic catalytic reaction. Results show that important coupling takes place between thermal and concentration fields. This coupling gives rise to unusual stabilizing or destabilizing effects, depending upon the value of Lewis number. Several examples are discussed. It is also shown how the results can be applied to other problems involving heat and mass transfer.
The ac losses of thin films of NbN have been measured on uncoated samples and samples coated with copper and aluminum. The reversibility of the superconducting to normal transition was studied under conditions of swept current at fixed field and swept field at fixed current. Results show that thin films of NbN can be stabilized by using normal metal overlays, and that ac losses in the stabilized material are substantially lower than those in the equivalent unstabilized material.
The spin-axis attitude stability in torque-free environment of dual-spin spacecrafts with energy losses in both bodies is studied by analytical means. A new mathematical model, which assumes the high speed rotor to be symmetrical, is introduced and analyzed. The linearized variational system of equations for the model with periodic coefficients is transformed to a kinematically similar autonomous system (according to Floquet and Liapunov) which can be analyzed routinely using established procedure. As an example, this technique is used on a recent mathematical model of the SAS-A spacecraft to establish steady state stability over a wide range of speeds.
A linearized stability analysis has been applied to a fluid flowing in a gravity field between horizontal planes in Couette flow under conditions such that the temperature of the bottom plane exceeds that of the top. It is shown that, under conditions likely to be encountered with polymer solutions, oscillatory instabilities will not be controlling. Criteria are offered for ascertaining when an analysis based upon a second-order fluid model may be expected to yield physically meaningful results. It is also shown that, for the fluid model considered, critical conditions for stability are not changed when disturbances which vary in the flow direction are substituted for those which are a function of the coordinate transverse to the flow.
The influence of a small parameter at the higher derivatives in the differential equations describing nonlinear systems of the Lur'e-Postnikov class on absolute stability in the parameter space is investigated. The conditions leading to singular perturbations of absolute stability are examined.
Investigation of the influence of heat transfer on the stability of a plane Poiseuille flow iahnnl. The liquid flow is affected by the heat transfer through the variation in viscosity with temperature. Additional viscosity gradient terms are included in a modified Orr-Sommerfeld equation, and it is the presence of these terms which leads to a prediction of more unstable flows, for without the inclusion of these extra terms, the flow is stabilized. The results show that a temperature difference between the walls is always destabilizing and, in particular, a temperature difference between the walls of 100 F leads to a reduction in the critical Reynolds number from 7800 to 4600.
Stability of various supported noble metal catalysts for initiation of the hydrogen-oxygen reaction was tested by means of steam-hydrogen treatment at 1000-1200 C followed by a simple activity test. Many catalysts were stable to 1100 C, but all lost some activity at 1200 C. The most active with very good stability was an iridium/alumina catalyst of high iridium content.
Development of a stability criterion of the Nyquist type from Michailov's criterion for a large class of distributed parameter systems, in particular, for a large class of transmission line systems with feedback. Following a generalization of Michailov's criterion, simplifying assumptions, usually valid in practice, are shown to yield a simplified test for determining whether 'encirclement-counting' constitutes a valid stability test. The results are reformulated for an open-loop analysis. Three examples show various aspects of the theoretical analysis.
The results of an analytical investigation of the rotational dynamics of a spinning Skylab space station are presented. The passive stability of motion of a simplified model consisting of a rigid core body with two attached flexible appendages is investigated. The parameter plane stability technique is applied to the specific Skylab case to determine its transient response to external disturbances.