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At least 1,351 records · Page 75
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NASA NTRS1989

Unsteady disturbances of streaming motions around bodies

The present investigation of flows around bodies with a stagnation point notes that the vortical part of such flows becomes singular along the entire body surface and its wake; as a result, the potential part of the flow will also be singular along the entire surface. A modified splitting of the velocity field is proposed which encompasses: (1) a vortical part having zero streamwise and normal components along the body surface; (2) an entropy-dependent part; and (3) a regular part similar to the potential part which satisfies a linear inhomogeneous wave equation with a modified source term.

Atassi, H. M.↗
NASA NTRS1989

Resonance in cylindrical-rectangular and wraparound microstrip structures

A rigorous analysis of the resonance frequency problem of both the cylindrical-rectangular and the wraparound microstrip structure is presented. The problem is formulated in terms of a set of vector integral equations. Using Galerkin's method to solve the integral equations, the complex resonance frequencies are studied with sinusoidal basis functions which incorporate the edge singularity. The complex resonance frequencies are computed using a perturbation approach. Modes suitable for resonator or antenna applications are investigated. The edge singularity of the patch current is shown to have no significant effect on the accuracy of the results. It is shown that the HE10 modes of the cylindrical-rectangular and wraparound patches are more appropriate for resonator applications. The HE01 and TE01 modes of the cylindrical-rectangular and wraparound patches, respectively, are efficient radiating modes.

Ali, Sami M.↗
NASA NTRS1990

Lower solar chromosphere-corona transition region. I - Theoretical models with small temperature gradients

A study of transition region models including the effects of classical thermal conduction, heating, and radiative cooling is carried out with attention directed toward the problem of understanding the observed emission in the lower transition region. It is found that the observationally inferred emission measure curve implies a near-balance between heating and radiative cooling in the lower transition region, and that the presence of strong hydrogen Ly-alpha cooling leads to the existence of singularities in the solutions of the force balance and energy balance equations when such a near-balance between heating and cooling is assumed. These singularities place strong constraints on the nature of viable models of the lower transition region and must be considered when Ly-alpha cooling is important. Previously suggested explanations of the observed emission from the lower transition region are considered in the context of the results of the present study, and conditions for the applicability of these suggested explanations are discussed.

Woods, D. Tod↗
NASA NTRS1990

Two-dimensional caustics in disturbed galaxy disks

Interacting galaxies show a variety of exotic morphologies besides the well-known rings, spirals, and bars. It is proposed that many of these can be identified with nonlinear, caustic structures that are known from singularity theory to be generic in collisionless dynamics. A simple kinematical model for stellar orbits is used to study the development of caustic waveforms in galaxy disks following impulsive, nonaxially symmetric (collisional) disturbances. It appears that all of the caustics known from singularity theory to be generic in two dimensions develop as transient forms in at least some moderately off-center collisions. The more complex, higher-order caustics appear most prominently in the more off-center and larger amplitude disturbances. It is further suggested that the highly nonlinear caustic waves may play an important role in interaction-induced star formation.

Struck-Marcell, Curtis↗
NASA NTRS1989

On the freestream matching condition for stagnation point turbulent flows

The problem of plane stagnation point flow with freestream turbulence is examined from a basic theoretical standpoint. It is argued that the singularity which arises from the standard kappa-epsilon model is not due to a defect in the model but results from the use of an inconsistent freestream boundary condition. The inconsistency lies in the implementation of a production equals dissipation equilibrium hypothesis in conjunction with a freestream mean velocity field that corresponds to homogeneous plane strain - a turbulent flow which does not reach such a simple equilibrium. Consequently, the adjustment that has been made in the constants of the epsilon-transport equation to eliminate this singularity is not self-consistent since it is tantamount to artificially imposing an equilibrium structure on a turbulent flow which is known not to have one.

Speziale, C. G.↗
NASA NTRS1990

Design of control laws for flutter suppression based on the aerodynamic energy concept and comparisons with other design methods

The aerodynamic energy method is used to synthesize control laws for NASA's drone for aerodynamic and structural testing-aerodynamic research wing 1 (DAST-ARW1) mathematical model. The performance of these control laws in terms of closed-loop flutter dynamic pressure, control surface activity, and robustness is compared with other control laws that relate to the same model. A control law synthesis technique that makes use of the return difference singular values is developed. It is based on the aerodynamic energy approach and is shown to yield results that are superior to those results given in the literature and are based on optimal control theory. Nyquist plots are presented, together with a short discussion regarding the relative merits of the minimum singular value as a measure of robustness as compared with the more traditional measure involving phase and gain margins.

Nissim, Eli↗
NASA NTRS1990

Estimability of geodetic parameters from space VLBI observables

The feasibility of space very long base interferometry (VLBI) observables for geodesy and geodynamics is investigated. A brief review of space VLBI systems from the point of view of potential geodetic application is given. A selected notational convention is used to jointly treat the VLBI observables of different types of baselines within a combined ground/space VLBI network. The basic equations of the space VLBI observables appropriate for convariance analysis are derived and included. The corresponding equations for the ground-to-ground baseline VLBI observables are also given for a comparison. The simplified expression of the mathematical models for both space VLBI observables (time delay and delay rate) include the ground station coordinates, the satellite orbital elements, the earth rotation parameters, the radio source coordinates, and clock parameters. The observation equations with these parameters were examined in order to determine which of them are separable or nonseparable. Singularity problems arising from coordinate system definition and critical configuration are studied. Linear dependencies between partials are analytically derived. The mathematical models for ground-space baseline VLBI observables were tested with simulation data in the frame of some numerical experiments. Singularity due to datum defect is confirmed.

Adam, Jozsef↗
NASA NTRS1990

Multirate sampled-data yaw-damper and modal suppression system design

A multirate control law synthesized algorithm based on an infinite-time quadratic cost function, was developed along with a method for analyzing the robustness of multirate systems. A generalized multirate sampled-data control law structure (GMCLS) was introduced. A new infinite-time-based parameter optimization multirate sampled-data control law synthesis method and solution algorithm were developed. A singular-value-based method for determining gain and phase margins for multirate systems was also developed. The finite-time-based parameter optimization multirate sampled-data control law synthesis algorithm originally intended to be applied to the aircraft problem was instead demonstrated by application to a simpler problem involving the control of the tip position of a two-link robot arm. The GMCLS, the infinite-time-based parameter optimization multirate control law synthesis method and solution algorithm, and the singular-value based method for determining gain and phase margins were all demonstrated by application to the aircraft control problem originally proposed for this project.

Berg, Martin C.↗
NASA NTRS1991

The surface and through crack problems in layered orthotropic plates

An analytical method is developed for a relatively accurate calculation of Stress Intensity Factors in a laminated orthotropic plate containing a through or part-through crack. The laminated plate is assumed to be under bending or membrane loading and the mode 1 problem is considered. First three transverse shear deformation plate theories (Mindlin's displacement based first-order theory, Reissner's stress-based first-order theory, and a simple-higher order theory due to Reddy) are reviewed and examined for homogeneous, laminated and heterogeneous orthotropic plates. Based on a general linear laminated plate theory, a method by which the stress intensity factors can be obtained in orthotropic laminated and heterogeneous plates with a through crack is developed. Examples are given for both symmetrically and unsymmetrically laminated plates and the effects of various material properties on the stress intensity factors are studied. In order to implement the line-spring model which is used later to study the surface crack problem, the corresponding plane elasticity problem of a two-bonded orthotropic plated containing a crack perpendicular to the interface is also considered. Three different crack profiles: an internal crack, an edge crack, and a crack terminating at the interface are considered. The effect of the different material combinations, geometries, and material orthotropy on the stress intensity factors and on the power of stress singularity for a crack terminating at the interface is fully examined. The Line Spring model of Rice and Levy is used for the part-through crack problem. The surface crack is assumed to lie in one of the two-layered laminated orthotropic plates due to the limitation of the available plane strain results. All problems considered are of the mixed boundary value type and are reduced to Cauchy type of singular integral equations which are then solved numerically.

Erdogan, Fazil↗
NASA NTRS1990

Constrained trajectory optimization for kinematically redundant arms

Two velocity optimization schemes for resolving redundant joint configurations are compared. The Extended Moore-Penrose Technique minimizes the joint velocities and avoids obstacles indirectly by adjoining a cost gradient to the solution. A new method can incorporate inequality constraints directly to avoid obstacles and singularities in the workspace. A four-link arm example is used to illustrate singularity avoidance while tracking desired end-effector paths.

Carignan, Craig R.↗
NASA NTRS1991

Optimal Control Problems with Switching Points

The main idea of this report is to give an overview of the problems and difficulties that arise in solving optimal control problems with switching points. A brief discussion of existing optimality conditions is given and a numerical approach for solving the multipoint boundary value problems associated with the first-order necessary conditions of optimal control is presented. Two real-life aerospace optimization problems are treated explicitly. These are altitude maximization for a sounding rocket (Goddard Problem) in the presence of a dynamic pressure limit, and range maximization for a supersonic aircraft flying in the vertical, also in the presence of a dynamic pressure limit. In the second problem singular control appears along arcs with active dynamic pressure limit, which in the context of optimal control, represents a first-order state inequality constraint. An extension of the Generalized Legendre-Clebsch Condition to the case of singular control along state/control constrained arcs is presented and is applied to the aircraft range maximization problem stated above. A contribution to the field of Jacobi Necessary Conditions is made by giving a new proof for the non-optimality of conjugate paths in the Accessory Minimum Problem. Because of its simple and explicit character, the new proof may provide the basis for an extension of Jacobi's Necessary Condition to the case of the trajectories with interior point constraints. Finally, the result that touch points cannot occur for first-order state inequality constraints is extended to the case of vector valued control functions.

Seywald, Hans↗
NASA NTRS1990

A rigid line inclusion at a bimaterial interface

A solution is presented for the plane elastostatics problem of a rigid line inclusion at a bimaterial interface. Explicit expressions are derived for the complex potentials. The complex stress intensity factors at the tip of the rigid line are compared with those for the corresponding crack problem. It is found that the nature of the singularities differ. Furthermore, unlike the crack problem, the singularity for the rigid line inclusion depends on the stresses parallel to the interface.

Ballarini, Roberto↗
NASA NTRS1990

Improved configuration control for redundant robots

This article presents a singularity-robust task-prioritized reformulation of the configuration control scheme for redundant robot manipulators. This reformulation suppresses large joint velocities near singularities, at the expense of small task trajectory errors. This is achieved by optimally reducing the joint velocities to induce minimal errors in the task performance by modifying the task trajectories. Furthermore, the same framework provides a means for assignment of priorities between the basic task of end-effector motion and the user-defined additional task for utilizing redundancy. This allows automatic relaxation of the additional task constraints in favor of the desired end-effector motion, when both cannot be achieved exactly. The improved configuration control scheme is illustrated for a variety of additional tasks, and extensive simulation results are presented.

Seraji, H.↗
NASA NTRS1991

Magellan in-flight gyro/star scanner misalignment calibration

Techniques are described for the in-flight calibration of gyro/star scanner misalignments for the Magellan spacecraft. The poor observability of one of the six components of misalignment is discussed in the context of a simple least-squares estimation model. The assumptions that lead to singularity in the information matrix are explicitly stated and it is shown that the singularity persists for all scanner slit configurations using only two slits, regardless of slit geometry or separation. A set of misalignment error state variables, a configuration of three stars, and a maneuver/scan sequence is described which yields a well-conditioned information matrix for least-squares estimation of five of the six misalignments. Finally, it is shown by convariance simulation that ground-based optimal estimation can satisfactorily resolve all six components of the misalignment error when more than two star scanner slits are used.

Boone, Jack N.↗
NASA NTRS1991

Robustness in the presence of mixed parametric uncertainty and unmodeled dynamics

Continuing the development of the structured singular value approach to robust control design, the authors investigate the problem of computing the structured singular value (mu) in the case of mixed real parametric and complex uncertainty. The problem is shown to be equivalent to a smooth constrained finite-dimensional optimization problem. In view of the fact that the functional to be maximized may have several local extrema, an upper bound on mu whose computation is numerically tractable is established; this leads to a sufficient condition of robust stability and performance. A historical perspective on the development of the mu theory is included.

Fan, Michael K. H.↗
NASA NTRS1991

Light-induced suppression of endogenous circadian amplitude in humans

A recent demonstration that the phase of the human circadian pacemaker could be inverted using an unconventional three-cycle stimulus has led to an investigation of whether critically timed exposure to a more moderate stimulus could drive that oscillator toward its singularity, a phaseless position at which the amplitude of circadian oscillation is zero. It is reported here that exposure of humans to fewer cycles of bright light, centered around the time at which the human circadian pacemaker is most sensitive to light-induced phase shifts, can markedly attenuate endogenous cicadian amplitude. In some cases this results in an apparent loss of rhythmicity, as expected to occur in the region of singularity.

Jewett, Megan↗
NASA NTRS1990

Kinematic analysis of 7 DOF anthropomorphic arms

A kinematic analysis of anthropomorphic seven-degree-of-freedom serial link spatial manipulators with revolute joints is presented. To uniquely determine joint angles for a given end-effector position and orientation, the redundancy is parameterized by a scalar variable which corresponds to the angle between the arm plane and a reference plane. The forward kinematic mappings from joint-space to end-effector coordinates and arm angle and the augmented Jacobian matrix which gives end-effector and arm angle rates as functions of joint rates are given. Conditions under which the augmented Jacobian becomes singular are given and are shown to correspond to the arm being either at a kinematically singular configuration or at a nonsingular configuration for which the arm angle ceases to parameterize the redundancy.

Kreutz-Delgado, K.↗
NASA NTRS1990

Scattering of impact wave by a crack in composite plate

The surface responses due to impact load on an infinite uniaxial graphite/epoxy plate with and without delamination cracks are investigated both in time and frequency domain by using a hybrid method combining the finite element discretization of the near-field with boundary integral representation of the field outside a contour enclosing completely the crack. This combined method leads to a set of linear unsymmetric complex matrix equations which are solved to obtain the response in the frequency domain by biconjugate gradient method. The time domain response is then obtained by using an FFT. In order to capture the time-domain characteristics accurately, high order finite elements have been used. Also, both the six node singular elements and eight node transition elements are used around the crack tips to model the crack-tip singularity. It is shown that from the numerical results for surface responses both depth and length of this crack can be identified.

Ju, T. H.↗