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A rigid rotor system coupled by a coulomb spline is modelled and analyzed by approximate analytical and numerical analytical methods. Expressions are derived for the variables of the resulting limit cycle and are shown to be quite accurate for a small departure from isotropy.
Coupling, developed for rotor of lift/cruise aircraft, employs two clutches for smooth transmission of power from gas-turbine engine to rotor. Prior to ascent, coupling applies friction-type transition clutch that accelerates rotor shaft to speeds matching those of engine shaft. Once shafts synchronized, spline coupling engaged and friction clutch released to provide positive mechanical drive.
The problem of identifying the spatially varying coefficient of elasticity using an observed solution to the forward problem is considered. Under appropriate conditions this problem can be treated as a first order hyperbolic equation in the unknown coefficient. Some continuous dependence results are developed for this problem and a spline-based technique is proposed for approximating the unknown coefficient, based on these results. The convergence of the numerical scheme is established and error estimates obtained.
Parameter and state estimation techniques for an elliptic system arising in a developmental model for the antenna surface in the Maypole Hoop/Column antenna are discussed. A computational algorithm based on spline approximations for the state and elastic parameters is given and numerical results obtained using this algorithm are summarized.
An optimum truncation level, N, in a spherical-harmonic analysis of the geomagnetic main field at the core-mantle boundary is determined by harmonic-spline analysis. Specifically, that value of N is found at which the two analyses are closest in a well defined sense and, for that value of N, the 'closeness' of two models is determined. Depending slightly on the definition of closeness, optimum N is found to be either 10 or 11. For those values the two analyses give remarkably similar results, showing that the conveniences of spherical harmonics can be retained with little penalty.
An algorithm is presented for determining the minimum curvature surface passing through a set of nonuniformly spaced data points. The curve is generated as a linear combination of Green functions for the biharmonic operator at each data point, with the amplitudes of the functions adjusted so that the interpolating surfaces passes through each point. The function passing through the points can be regarded as a spline to which point forces are applied, defining the minimum curvature between the points. The technique was used to combine the along track slopes of the GEOS-3 and Seasat altimeter data into a consistent geoid height map of the Caribbean area, covering 0.5 million data points in the process. Sample images are provided and new topographic features that are revealed are discussed.
The secular variation of the earth's magnetic field is itself subject to temporal variations. These are investigated with the aid of the coefficients of a series of spherical harmonic models of secular variation deduced from data for the interval 1903-1982 from the worldwide network of magnetic observatories. For some studies it is convenient to approximate the time variation of the spherical harmonic coefficients with a smooth, continuous, function; for this a spline fitting is used. The phenomena that are investigated include periodicities, discontinuities, and correlation with the length of day. The numerical data presented will be of use for further investigations and for the synthesis of secular variation at any place and at any time within the interval of the data - they are not appropriate for temporal extrapolations.
A new method, based on partial spline models, is developed for including specified discontinuities in otherwise smooth two- and three-dimensional objective analyses. The method is appropriate for including tropopause height information in two- and three-dimensinal temperature analyses, using the O'Sullivan-Wahba physical variational method for analysis of satellite radiance data, and may in principle be used in a combined variational analysis of observed, forecast, and climate information. A numerical method for its implementation is described and a prototype two-dimensional analysis based on simulated radiosonde and tropopause height data is shown. The method may also be appropriate for other geophysical problems, such as modeling the ocean thermocline, fronts, discontinuities, etc.
A parameter-estimation technique for boundary-integral equations of the second kind is developed. The output least-squares identification technique using the spline collocation method is considered. The convergence analysis for the numerical method is discussed. The results are applied to boundary parameter estimations for two-dimensional Laplace and Helmholtz equations.
The problem of identifying the spatially varying coefficient of elasticity using an observed solution to the forward problem is considered. Under appropriate conditions this problem can be treated as a first order hyperbolic equation in the unknown coefficient. Some continuous dependence results are developed for this problem and a spline-based technique is proposed for approximating the unknown coefficient, based on these results. The convergence of the numerical scheme is established and error estimates obtained.
It is shown how a variable structure control technique could be implemented to achieve precise pointing and good tracking of a deformable structure subject to fast slewing maneuvers. The correction torque that has to be applied to the structure is based on estimates of upper bounds on the model errors. For a rapid rotation of the deformable structure, the elastic response can be modeled by oscillators driven by angular acceleration, and where stiffness and damping coefficients are also angular velocity and acceleration dependent. By transforming this slew-driven elastic dynamics into bilinear form (be regarding the vector made up of the angular velocity, squared angular velocity and angular acceleration components, which appear in the coefficients as the input to the deformation dynamics), an operator spline can be constructed, that gives a low order estimate of the induced disturbance. Moreover, a worst case error bound between the estimated deformation and the unknown exact deformation is also generated, which can be used where required in the sliding control correction.
An efficient algorithm for computing the generalized cross-validation function for the general cross-validated regularization/smoothing problem is provided. This algorithm is appropriate for problems where no natural structure is available, and the regularization/smoothing problem is solved (exactly) in a reproducing kernel Hilbert space. It is particularly appropriate for certain multivariate smoothing problems with irregularly spaced data, and certain remote sensing problems, such as those that occur in meteorology, where the sensors are arranged irregularly. The algorithm is applied to the fitting of interaction spline models with irregularly spaced data and two smoothing parameters; favorable timing results are presented. The algorithm may be extended to the computation of certain generalized maximum likelihood (GML) functions. Application of the GML algorithm to a problem in numerical weather forecasting, and to a broad class of hypothesis testing problems, is noted.
G/SPLINES are a hybrid of Friedman's Multivariable Adaptive Regression Splines (MARS) algorithm with Holland's Genetic Algorithm. In this hybrid, the incremental search is replaced by a genetic search. The G/SPLINE algorithm exhibits performance comparable to that of the MARS algorithm, requires fewer least squares computations, and allows significantly larger problems to be considered.
A fastener was developed by NASA Goddard for efficiently performing assembly, maintenance, and equipment replacement functions in space using either robotic or astronaut means. This fastener, the 'Spline Locking Screw' (SLS) would also have significant commercial value in advanced manufacturing. Commercial (or DoD) products could be manufactured in such a way that their prime subassemblies would be assembled using SLS fasteners. This would permit machines and robots to disconnect and replace these modules/parts with ease, greatly reducing life cycle costs of the products and greatly enhancing the quality, timeliness, and consistency of repairs, upgrades, and remanufacturing. The operation of the basic SLS fastener is detailed, including hardware and test results. Its extension into a comprehensive fastening strategy for NASA use in space is also outlined. Following this, the discussion turns toward potential commercial and government applications and the potential market significance of same.
An algebraic adaptive grid system based on equidistribution law and utilized by the Non-Uniform Rational B-Spline (NURBS) surface for redistribution is presented. A weight function, utilizing a properly weighted boolean sum of various flow field characteristics is developed. Computational examples are presented to demonstrate the success of this technique.
A fastener was developed by NASA Goddard for efficiently performing assembly, maintenance, and equipment replacement functions in space using either robotics or astronaut means. This fastener, the 'Spline Locking Screw' (SLS) would also have significant commercial value in advanced space manufacturing. Commercial (or DoD) products could be manufactured in such a way that their prime subassemblies would be assembled using SLS fasteners. This would permit machines and robots to disconnect and replace these modules/parts with ease, greatly reducing life cycle costs of the products and greatly enhancing the quality, timeliness, and consistency of repairs, upgrades, and remanufacturing. The operation of the basic SLS fastener is detailed, including hardware and test results. Its extension into a comprehensive fastening strategy for NASA use in space is also outlined. Following this, the discussion turns toward potential commercial and government applications and the potential market significance of same.
A geometric method is proposed for fitting rational cubic B-spline curves to data that represent smooth curves including intersection or silhouette lines. The algorithm is based on the convex hull and the variation diminishing properties of Bezier/B-spline curves. The algorithm has the following structure: it tries to fit one Bezier segment to the entire data set and if it is impossible it subdivides the data set and reconsiders the subset. After accepting the subset the algorithm tries to find the longest run of points within a tolerance and then approximates this set with a Bezier cubic segment. The algorithm uses this procedure repeatedly to the rest of the data points until all points are fitted. It is concluded that the algorithm delivers fitting curves which approximate the data with high accuracy even in cases with large tolerances.
Interlocking fine-pitch ribs and grooves formed on otherwise flat mating end faces of housing and outer race of rolling-element bearing to be mounted in housing, according to proposal. Splines bear large torque loads and impose minimal distortion on raceway.