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NASA NTRS1985

Midlatitude tropical interactions during winter

Pre-FGGE and FGGE/MONEX data are used to identify short term midlatitude tropical and longitudinal interactions during the winter monsoon. These interactions occur as cold surges, which develop over the East Asian continent and penetrate deep into the tropics with fast gravity wave speed. The observed interactions that occur after a surge include cyclogenesis and enhanced convection in the equatorial region, feedback from equatorial convection to midlatitude circulation systems, tropical east-west (Walker) circulations, and cross-equatorial influence. These interactions are also studied theoretically by analytical solutions of linearized shallow water equations. Response to transient forcing (monsoon surges) are mainly in Rossby and Kelvin modes. When the forcing time scale is short, significant gravity modes are also excited. The responses closely resemble observed winter monsoon flow. Responses to stationary forcing show that deep (barotropic) motions propagate energy away into high latitudes and that shallow (baroclinic) motions are trapped around the equator. It is shown that the barotropic teleconnection-type response to tropical sources found in previous numerical studies was due to the specified vertical wind shear and surface friction.

Chang, C. P.↗

NASA NTRS1988

Three-dimensional adaptive grid generation for body-fitted coordinate system

This report describes a numerical method for generating 3-D grids for general configurations. The basic method involves the solution of a set of quasi-linear elliptic partial differential equations via pointwise relaxation with a local relaxation factor. It allows specification of the grid spacing off the boundary surfaces and the grid orthogonality at the boundary surfaces. It includes adaptive mechanisms to improve smoothness, orthogonality, and flow resolution in the grid interior.

Chen, S. C.↗

NASA NTRS1988

A novel approach to the modelling and control of flexible robot arms

A general dynamic model of a two-link Euler-Bernoulli beam flexible robot arm is presented in the form of partial-differential-integral equations. Observations are made on important properties of the dynamic model. The resulting infinite-dimensional system is then input-output decoupled and partially linearized by a diffeomorphic state transformation and nonlinear state feedback. The local stability issue is addressed for a one-link flexible robot arm.

Ding, Xuru↗

NASA NTRS1988

Three-dimensional adaptive grid generation for body-fitted coordinate system

Chen, S. C.↗

NASA NTRS1990

Control/structure interaction - Effects of actuator dynamics

The present evaluation of the effects of including actuator dynamics in the formulation of simple control laws for vibration suppression leads, theoretically, to a prediction of substantial interaction between actuator dynamics, structural dynamics, and control-law choices. Attention is given to the problem of closed-loop instability, under the assumptions that (1) the structure is modeled by an asymptotically stable system, (2) vibration-suppression is the purpose of control, and (3) the structure is well modeled by a finite-dimensional linear set of equations with viscous damping, such as a FEM model.

Inman, Daniel J.↗

NASA NTRS1991

Improved solution for ill-conditioned algebraic equations by epsilon decomposition

Matrix eigenvalue theory is presently used to examine the source of ill-conditioning in linear algebraic equations; the approach highlights the critical role played by the zero and near-zero eigenvalues and corresponding eigenvectors of poorly-conditioned systems. Insights derived from this approach are used to improve the recently developed epsilon-decomposition (E-D) solution procedure. The efficiency of E-D is significant for large matrices possessing small rank deficiency.

Ojalvo, Irving U.↗

NASA NTRS2004

Proceedings from the 2nd International Symposium on Formation Flying Missions and Technologies

Topics discussed include: The Stellar Imager (SI) "Vision Mission"; First Formation Flying Demonstration Mission Including on Flight Nulling; Formation Flying X-ray Telescope in L2 Orbit; SPECS: The Kilometer-baseline Far-IR Interferometer in NASA's Space Science Roadmap Presentation; A Tight Formation for Along-track SAR Interferometry; Realization of the Solar Power Satellite using the Formation Flying Solar Reflector; SIMBOL-X : Formation Flying for High-Energy Astrophysics; High Precision Optical Metrology for DARWIN; Close Formation Flight of Micro-Satellites for SAR Interferometry; Station-Keeping Requirements for Astronomical Imaging with Constellations of Free-Flying Collectors; Closed-Loop Control of Formation Flying Satellites; Formation Control for the MAXIM Mission; Precision Formation Keeping at L2 Using the Autonomous Formation Flying Sensor; Robust Control of Multiple Spacecraft Formation Flying; Virtual Rigid Body (VRB) Satellite Formation Control: Stable Mode-Switching and Cross-Coupling; Electromagnetic Formation Flight (EMFF) System Design, Mission Capabilities, and Testbed Development; Navigation Algorithms for Formation Flying Missions; Use of Formation Flying Small Satellites Incorporating OISL's in a Tandem Cluster Mission; Semimajor Axis Estimation Strategies; Relative Attitude Determination of Earth Orbiting Formations Using GPS Receivers; Analysis of Formation Flying in Eccentric Orbits Using Linearized Equations of Relative Motion; Conservative Analytical Collision Probabilities for Orbital Formation Flying; Equations of Motion and Stability of Two Spacecraft in Formation at the Earth/Moon Triangular Libration Points; Formations Near the Libration Points: Design Strategies Using Natural and Non-Natural Ares; An Overview of the Formation and Attitude Control System for the Terrestrial Planet Finder Formation Flying Interferometer; GVE-Based Dynamics and Control for Formation Flying Spacecraft; GNC System Design for a New Concept of X-Ray Distributed Telescope; GNC System for the Deployment and Fine Control of the DARWIN Free-Flying Interferometer; Formation Algorithm and Simulation Testbed; and PLATFORM: A Formation Flying, RvD and Robotic Validation Test-bench.

Source record↗

NASA NTRS1985

A new approach to approximating the linear quadratic optimal control law for hereditary systems with control delays

A factorization approach is presented for deriving approximations to the optimal feedback gain for the linear regulator-quadratic cost problem associated with time-varying functional differential equations with control delays. The approach is based on a discretization of the state penalty which leads to a simple structure for the feedback control law. General properties of the Volterra factors of Hilbert-Schmidt operators are then used to obtain convergence results for the feedback kernels.

Milman, M. H.↗

NASA NTRS1985

Numerical solution of Euler's equation by perturbed functionals

A perturbed functional iteration has been developed to solve nonlinear systems. It adds at each iteration level, unique perturbation parameters to nonlinear Gauss-Seidel iterates which enhances its convergence properties. As convergence is approached these parameters are damped out. Local linearization along the diagonal has been used to compute these parameters. The method requires no computation of Jacobian or factorization of matrices. Analysis of convergence depends on properties of certain contraction-type mappings, known as D-mappings. In this article, application of this method to solve an implicit finite difference approximation of Euler's equation is studied. Some representative results for the well known shock tube problem and compressible flows in a nozzle are given.

Dey, S. K.↗

NASA NTRS1962

Rendezvous Guidance Technology

The literature on rendezvous guidance technology is reviewed and a bibliography of about 160 documents is presented. The importance of the proper selection of the ascent trajectory and of the orbit for a manned space station or an orbiting launch complex is emphasized. The way the launch delay problem affects the selection of the ascent trajectory and the target orbit is discussed. A specific ascent trajectory and an orbit for a manned space station or an orbiting launch complex is recommended on the premise that launch delay problems will continue to outweigh most of the other orbit selection criteria. A new method for determining the velocity corrections required for mid-course guidance is proposed . The proposed methods consist of an "exact-numerical" solution of the relative equations of motion in the "Shell-coordinate system." The proposed "exact-numerical" method extends the applicability of the mid- course equations to a much greater range than that of the currently available linear methods .

Trajectory↗

NASA NTRS1971

Ordinary-mode electromagnetic instability in colliding plasma streams.

The instability of the electromagnetic linearly polarized mode propagating perpendicularly to the magnetic field is studied for a system composed of two colliding plasma streams, in each of which the electrons and ions are streaming at the same velocity. Using linearized Vlasov-Maxwell equations and allowing for anisotropic temperatures, it is found that in the presence of streaming ions the instability can occur in very low-beta plasmas. The plasma is increasingly susceptible to the electromagnetic instability with increasing values of beta, streaming velocity, temperature ratio of parallel to perpendicular electrons, and temperature ratio of perpendicular electrons to perpendicular ions.

Lee, K. F.↗

NASA NTRS1973

A study of the effect of a boundary layer profile on the dynamic response and acoustic radiation of flat panels

The response of a thin, elastic plate to a harmonic force which drives the plate from below and a compressible air stream with a viscous boundary layer flowing parallel to the upper surface along the length was investigated. Equations governing the forced response of the coupled plate-aerodynamic system are derived along with appropriate boundary conditions. Calculations of basic solution parameters for a linear velocity profile and for a Blasius profile showed that the same system response could be obtained from each profile if appropriate values of boundary layer thickness were chosen for each profile.

Mixson, J. S.↗

NASA NTRS1975

Application of Hamilton's law of varying action

The law of varying action enunciated by Hamilton in 1834-1835 permits the direct analytical solution of the problems of mechanics, both stationary and nonstationary, without consideration of force equilibrium and the theory of differential equations associated therewith. It has not been possible to obtain direct analytical solutions to nonstationary systems through the use of energy theory, which has been limited for 140 years to the principle of least action and to Hamilton's principle. It is shown here that Hamilton's law permits the direct analytical solution to nonstationary, initial value systems in the mechanics of solids without any knowledge or use of the theory of differential equations. Solutions are demonstrated for nonconservative, nonstationary particle motion, both linear and nonlinear.

Bailey, C. D.↗

NASA NTRS1980

Reduced-order Kalman filtering with incomplete observability

Kalman filtering is considered with reference to linear stochastic dynamic systems without complete observability. It is shown that the canonical decomposition theorem can be extended to the stochastic case and the matrix Riccati equation of the Kalman filter is order-reducible if some states are not observable. The inclusion of unobservable states in Kalman filtering makes the unobservable states 'asymptotically' observable in the filter if these unobservable states are dynamically connected to observable states and asymptotically stable. The reduced-order Kalman filter saves computation time when compared to the conventional Kalman filter.

Yonezawa, K.↗

NASA NTRS1981

A modified Dodge algorithm for the parabolized Navier-Stokes equation and compressible duct flows

A revised version of Dodge's split-velocity method for numerical calculation of compressible duct flow was developed. The revision incorporates balancing of mass flow rates on each marching step in order to maintain front-to-back continuity during the calculation. The (checkerboard) zebra algorithm is applied to solution of the three dimensional continuity equation in conservative form. A second-order A-stable linear multistep method is employed in effecting a marching solution of the parabolized momentum equations. A checkerboard iteration is used to solve the resulting implicit nonlinear systems of finite-difference equations which govern stepwise transition. Qualitive agreement with analytical predictions and experimental results was obtained for some flows with well-known solutions.

Cooke, C. H.↗

NASA NTRS1981

Bifurcation and post-buckling analysis of laminated composite plates via reduced basis technique

A reduced basis technique and a problem-adaptive computational algorithm are presented for the bifurcation and post-buckling analysis of laminated anisotropic plates. The computational algorithm can be conveniently divided into three distinct stages. The first stage is that of determining the bifurcation point. The plate is discretized by using displacement finite element (or finite difference) models. The special symmetries exhibited by the response of the anisotropic plate are used to reduce the size of the analysis region. The vector of unknown nodal parameters is expressed as a linear combination of a small number of basis vectors, and a Rayleigh-Ritz technique is used to approximate the finite element equations by a small system of algebraic equations. The reduced equations are used to determine the bifurcation point and the associated eigenmode of the panel. In the second stage of the bifurcation buckling mode is used to obtain a nonlinear solution in the vicinity of the bifurcation point and new (updated) sets of basis vectors and reduced equations are generated. In the third stage the reduced equations are used to trace the post-buckling paths. The effectiveness of the proposed technique for predicting the bifurcation and post-buckling behavior of plates is demonstrated by means of numerical examples for plates loaded by means of prescribed edge displacements.

Noor, A. K.↗

NASA NTRS1983

Flight in low-level wind shear

Results of studies of wind shear hazard to aircraft operation are summarized. Existing wind shear profiles currently used in computer and flight simulator studies are reviewed. The governing equations of motion for an aircraft are derived incorporating the variable wind effects. Quantitative discussions of the effects of wind shear on aircraft performance are presented. These are followed by a review of mathematical solutions to both the linear and nonlinear forms of the governing equations. Solutions with and without control laws are presented. The application of detailed analysis to develop warning and detection systems based on Doppler radar measuring wind speed along the flight path is given. A number of flight path deterioration parameters are defined and evaluated. Comparison of computer-predicted flight paths with those measured in a manned flight simulator is made. Some proposed airborne and ground-based wind shear hazard warning and detection systems are reviewed. The advantages and disadvantages of both types of systems are discussed.

Frost, W.↗

NASA NTRS1983

A modified Dodge algorithm for the parabolized Navier-Stokes equations and compressible duct flows

A revised version of Dodge's split-velocity method for numerical calculation of compressible duct flow was developed. The revision incorporates balancing of mass flow rates on each marching step in order to maintain front-to-back continuity during the calculation. The (checkerboard) zebra algorithm is applied to solution of the three dimensional continuity equation in conservative form. A second-order A-stable linear multistep method is employed in effecting a marching solution of the parabolized momentum equations. A checkerboard iteration is used to solve the resulting implicit nonlinear systems of finite-difference equations which govern stepwise transition. Qualitative agreement with analytical predictions and experimental results was obtained for some flows with well-known solutions. Previously announced in STAR as N82-16363

Cooke, C. H.↗