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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Attitude determination using vector observations: A fast optimal matrix algorithm

The attitude matrix minimizing Wahba's loss function is computed directly by a method that is competitive with the fastest known algorithm for finding this optimal estimate. The method also provides an estimate of the attitude error covariance matrix. Analysis of the special case of two vector observations identifies those cases for which the TRIAD or algebraic method minimizes Wahba's loss function.

Markley, F. Landis↗
NASA NTRS1993

Attitude determination using vector observations - A fast optimal matrix algorithm

The attitude matrix minimizing Wahba's loss function is computed directly by a method that is competitive with the fastest known algorithm for finding this optimal estimate. The method also provides an estimate of the attitude error covariance matrix. Analysis of the special case of two vector observations identifies those cases for which the TRIAD or algebraic method minimizes Wahba's loss function.

Markley, F. L.↗
NASA NTRS1983

Three-dimensional algebraic grid generation

One of the major approaches to numerical grid generation is the explicit algebraic expression of a physical grid as a function of a uniform grid in a rectangular computational coordinate system. The algebraic methods are based on mathematical interpolation, and the primary advantages are speed and directness. The relation between interpolation and grid generation is described. For three-dimensional grid generation, transfinite interpolation using the coordinate control processes developed in the multisurface method and two-boundary technique are advocated. Grid singularities encountered in three dimensions are discussed, and the exploration of multiple overlapping grids is proposed. Some aspects of interactive algebraic grid computation in three dimensions are discussed.

Smith, R. E.↗
NASA NTRS1991

An adaptive grid method for computing time accurate solutions on structured grids

The solution method consists of three parts: a grid movement scheme; an unsteady Euler equation solver; and a temporal coupling routine that links the dynamic grid to the Euler solver. The grid movement scheme is an algebraic method containing grid controls that generate a smooth grid that resolves the severe solution gradients and the sharp transitions in the solution gradients. The temporal coupling is performed with a grid prediction correction procedure that is simple to implement and provides a grid that does not lag the solution in time. The adaptive solution method is tested by computing the unsteady inviscid solutions for a one dimensional shock tube and a two dimensional shock vortex iteraction.

Bockelie, Michael J.↗
NASA NTRS1975

Numerical methods for evaluating the derivatives of eigenvalues and eigenvectors

Two numerical methods are presented for computing the derivatives of eigenvalues and eigenvectors which do not require complete solution of the eigenvalue problem if only a few derivatives are sought. The 'iterative' method may be used to find the first derivative of one or all of the eigenvectors together with the second derivative of their eigenvalues in a self-adjoint system. If the left- and right-hand eigenvectors are known, the first derivative of the eigenvector corresponding to the largest eigenvalue and the second derivative of the largest eigenvalue may be obtained for a nonself-adjoint system. The 'algebraic' method may be used to find all orders of the derivatives, provided they exist, without requiring the left-hand eigenvectors.

Rudisill, C. S.↗
NASA NTRS1972

Lie algebras and linear differential equations.

Certain symmetry properties possessed by the solutions of linear differential equations are examined. For this purpose, some basic ideas from the theory of finite dimensional linear systems are used together with the work of Wei and Norman on the use of Lie algebraic methods in differential equation theory.

Brockett, R. W.↗
NASA NTRS1980

A remarkable operator version of the Navier-Stokes equation

The Navier-Stokes equation is transformed into a closed nonlinear equation for the convected curl operator. It is shown how Lie algebraic methods can be employed to solve the obtained double-commutator equation. The proposed operator equation provides a way to the further development of the Navier-Stokes fluid flow theory.

Rosen, G.↗
NASA NTRS1980

Three dimensional spline-generated coordinate transformations for grids around wing-body configurations

A direct algebraic method was developed and applied to generate three dimensional grids around wing-body configurations. The method used is a generalized transfinite interpolation method which generates the desired coordinate transformation using geometric data only on the boundaries of the domain of interest. The geometric data that can be specified includes not only coordinates on the boundaries but also out-of-surface parametric derivatives that give a very precise control over the transformation in the vicinity of the surface. In addition to this, the method gives good control over the stretching of the mesh between different boundaries.

Eriksson, L. E.↗
NASA NTRS1983

Vector-algebra approach to extract Denavit-Hartenberg parameters of assembled robot arms

The Denavit-Hartenberg parameters characterize the joint axis systems in a robot arm and, naturally, appear in the transformation matrices from one joint axis system to another. These parameters are needed in the control of robot arms and in the passage of sensor information along the arm. This paper presents a vector algebra method to determine these parameters for any assembled robot arm. The idea is to measure the location of the robot hand (or extension) for different joint angles and then use these measurements to calculate the parameters.

Barker, L. K.↗
NASA NTRS1984

A hydromagnetic model of corotating conductive solar wind streams

Under the assumption of quasi-azimuthal symmetry the governing equations of a steady hydromagnetic flow in a thermally conductive flux tube possess six invariants. Four of them represent constancy of mass efflux, energy efflux, angular momentum efflux and magnetic flux. Based on the entropy equation we obtain useful approximation in explicit expressions for the two remaining invariants. One of them provides the constraint which determines the compatible heat flux to ensure a vanishing pressure at infinity. Thus, the admissible solution that represents a corotating solar wind stream in terms of specified interplanetary condition can be calculated by an algebraic method, without the necessity of numerical integration. A two-point relationship is then derived, which correlates the solar wind properties at two separated interplanetary sites measured at two properly separated instants. This relationship may be applied to observational data from spacecraft and earth-bound satellites to discern the corotation feature in the solar wind.

Yeh, T.↗
NASA NTRS1986

Computing Relative Joint Positions of Robot Arms

Vector-algebra method developed for extracting Denavit-Hartenberg parameters for any assembled robot arm. Method for extracting relative joint geometry of robot arms useful to researchers who need data for existing robot arms for either validation of mathematical models or for studies involving actual control of these devices. Method, does not require robot arm to be disassembled, also useful in recalibration of misalined or bent robot arm and becomes useful industrial procedure. Merit of method is errors not propagated.

Barker, L. K.↗
NASA NTRS1986

Modified Denavit-Hartenberg parameters for better location of joint axis systems in robot arms

The Denavit-Hartenberg parameters define the relative location of successive joint axis systems in a robot arm. A recent justifiable criticism is that one of these parameters becomes extremely large when two successive joints have near-parallel rotational axes. Geometrically, this parameter then locates a joint axis system at an excessive distance from the robot arm and, computationally, leads to an ill-conditioned transformation matrix. In this paper, a simple modification (which results from constraining a transverse vector between successive joint rotational axes to be normal to one of the rotational axes, instead of both) overcomes this criticism and favorably locates the joint axis system. An example is given for near-parallel rotational axes of the elbow and shoulder joints in a robot arm. The regular and modified parameters are extracted by an algebraic method with simulated measurement data. Unlike the modified parameters, extracted values of the regular parameters are very sensitive to measurement accuracy.

Barker, L. K.↗
NASA NTRS1986

Euler solutions for high-speed flow about complex three-dimensional configurations

A numerical algorithm based on a finite-volume explicit scheme with Runge-Kutta time integration of the Euler equations is presented for calculating high-speed three-dimensional flow about complex aerospace configurations. The use of enhancing factors such as artificial dissipative terms, enthalpy damping and local time-stepping are described. An algebraic method for generating quasi-three-dimensional computational grids for realistic aerospace configurations is presented. Computed results for various three-dimensional bodies at different Mach numbers and angles of attack have been obtained using the methods for grid-generation and flow simulation. Comparison of computed and experimental data for an advanced tactical aircraft-like configuration is presented, and a reasonable agreement of the data is noticed.

Moitra, A.↗
NASA NTRS1987

Robustness issues in boundary feedback of flexible structures

Transfer function models for basic structural elements with boundary control reveal certain inherent properties relevant to questions of control system realization, design, and analysis of robustness. The transfer functions involved are not strictly proper, may be nonminimum phase (except for the special case of colocated actuation and sensing), and often have large number of poles on the imaginary axis. In this paper these basic questions are considered in terms of modeling and control system design for robustness. The application of algebraic methods for computing stabilizing control, based on certain exact, irrational transfer functions is investigated. Boundary control of the wave equation is considered and extension of the method to more general problems is suggested. Special attention is given to implementation issues associated with a class of infinite dimensional control laws.

Bennett, W. H.↗
NASA NTRS1991

Implementation of control point form of algebraic grid-generation technique

The control point form (CPF) provides explicit control of physical grid shape and grid spacing through the movement of the control points. The control point array, called a control net, is a space grid type arrangement of locations in physical space with an index for each direction. As an algebraic method CPF is efficient and works well with interactive computer graphics. A family of menu-driven, interactive grid-generation computer codes (TURBO) is being developed by using CPF. Key features of TurboI (a TURBO member) are discussed and typical results are presented. TurboI runs on any IRIS 4D series workstation.

Choo, Yung K.↗
NASA NTRS1992

GridMan: A grid manipulation system

GridMan is an interactive grid manipulation system. It operates on grids to produce new grids which conform to user demands. The input grids are not constrained to come from any particular source. They may be generated by algebraic methods, elliptic methods, hyperbolic methods, parabolic methods, or some combination of methods. The methods are included in the various available structured grid generation codes. These codes perform the basic assembly function for the various elements of the initial grid. For block structured grids, the assembly can be quite complex due to a large number of clock corners, edges, and faces for which various connections and orientations must be properly identified. The grid generation codes are distinguished among themselves by their balance between interactive and automatic actions and by their modest variations in control. The basic form of GridMan provides a much more substantial level of grid control and will take its input from any of the structured grid generation codes. The communication link to the outside codes is a data file which contains the grid or section of grid.

Eiseman, Peter R.↗