An attempt to solve differential equations symbolically
Writing programs in interactive FORMAC language to implement Picard iteration in solving systems of ordinary differential equations
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Writing programs in interactive FORMAC language to implement Picard iteration in solving systems of ordinary differential equations
Algorithm for solving Popov stability criterion applied to sampled data systems
Variants of secant method for solving nonlinear system of equations comprising algorithms and related convergence techniques
Numerical method and FORTRAN program for solving Poisson's equation over axisymmetric regions of spherical body
Modified quasilinearization algorithm for solving nonlinear equations
Computer program HETRAN to solve two dimensional steady state heat conduction on cladded tube with connecting fin
Modified perturbation method for solving optimal control boundary value problems with state variable inequality constraints, noting application to reentry trajectories
A technique for solving n-dimensional games is developed and applied to two pursuit-evasion games. The first is a two-dimensional game similar to the homicidal chauffeur but modified to resemble an airplane-helicopter engagement. The second is a five-dimensional game of two airplanes at constant altitude and with thrust and turning controls. The performance function to be optimized by the pursuer and evader was the distance between the evader and a given target point in front of the pursuer. The analytic solution to the first game reveals that both unique and nonunique solutions exist. A comparison between the gradient results and the analytic solution shows a dependence on the nominal controls in regions where nonunique solutions exist. In the unique solution region, the results from the two methods agree closely. The results for the five-dimensional two-airplane game are also shown to be dependent on the nominal controls selected and indicate that initial conditions are in a region of nonunique solutions.
Continuing research is reported in a program aimed at the development of a robot computer problem solving system. The motivation and results are described of a theoretical investigation concerning the general properties of behavioral systems. Some of the important issues which a general theory of behavioral organization should encompass are outlined and discussed.
The application of NASA management approach to solving complex problems on earth is discussed. The management of the Apollo program is presented as an example of effective management techniques. Four key elements of effective management are analyzed. Photographs of the Cape Kennedy launch sites and supporting equipment are included to support the discussions.
This algorithm is an extension of Moler and Stewart's QZ algorithm with some added features for saving time and operations. Also, some additional properties of the QR algorithm which were not practical to implement in the QZ algorithm can be generalized with the combination shift QZ algorithm. Numerous test cases are presented to give practical application tests for algorithm. Based on results, this algorithm should be preferred over existing algorithms which attempt to solve the class of generalized eigenproblems where both matrices are singular or nearly singular.
A robot computer problem solving system which represents a robot exploration vehicle in a simulated Mars environment is described. The model exhibits changes and improvements made on a previously designed robot in a city environment. The Martian environment is modeled in Cartesian coordinates; objects are scattered about a plane; arbitrary restrictions on the robot's vision have been removed; and the robot's path contains arbitrary curves. New environmental features, particularly the visual occlusion of objects by other objects, were added to the model. Two different algorithms were developed for computing occlusion. Movement and vision capabilities of the robot were established in the Mars environment, using LISP/FORTRAN interface for computational efficiency. The graphical display program was redesigned to reflect the change to the Mars-like environment.
Two-man teams solved credible, 'real-world' problems for which computer assistance has been or could be useful. Conversations were carried on in one of four modes of communication: (1) typewriting, (2) handwriting, (3) voice, and (4) natural, unrestricted communication. Two groups of subjects (experienced and inexperienced typists) were tested in the typewriting mode. Performance was assessed on three classes of dependent measures: time to solution, behavioral measures of activity, and linguistic measures. Significant and meaningful differences among the communication modes were found in each of the three classes of dependent variable. This paper is concerned mainly with the results of the activity analyses. Behavior was recorded in 15 different categories. The analyses of variance yielded 34 statistically significant terms of which 27 were judged to be practically significant as well. When the data were transformed to eliminate heterogeneity, the analyses of variance yielded 35 statistically significant terms of which 26 were judged to be practically significant.
A description of and user's manual are presented for one of a group of FORTRAN programs which, together, can be used for the analysis and design of wings in steady, subsonic flow according to a kernel function method lifting surface theory. This particular program is the one which solves the sets of simultaneous, linear, algebraic equations arising from the thin wing analysis. This program has the capability of striking out rows and columns of the aerodynamic influence matrix and rows of the associated boundary condition vectors (right hand sides). This capability significantly enhances the effectiveness of the kernel function method of lifting surface theory because studies of the convergence of solutions with the number of control points can be done with the calculation of only a single influence matrix.
The conceptual, experimental, and practical phases of developing a robot computer problem solving system are outlined. Robot intelligence, conversion of the programming language SAIL to run under the THNEX monitor, and the use of the network to run several cooperating jobs at different sites are discussed.
Some methods of approaching a solution to the Hamilton-Jacobi equation are outlined and examples are given to illustrate particular methods. These methods may be used for cases where the Hamilton-Jacobi equation is not separable and have been particularly useful in solving the rigid body motion of an earth satellite subjected to gravity torques. These general applications may also have usefulness in studying the motion of satellites with aerodynamic torque and in studying space vehicle motion where thrusting is involved.
Several numerical integration techniques for solving common aeronomic problems involving species rate equations are compared for speed and accuracy. A newer technique that defines families of species that are nearly conserved is found to be superior to an iterative technique when both methods are applied to simple test problems. The 'conservation' technique is also found to be more economical than the more complex Gear (1969) integration scheme for comparable accuracy.
Various current and future problem areas of marine geodesy are identified. These oceanic problem areas are highly diversified and include submersible navigation under ice seas, demarcation and determination of boundaries in deep ocean, tsunamis, ecology, etc., etc. Their achieved as well as desired positional accuracy estimates, based upon publications and discussions, are also given. A multipurpose approach to solve these problems is described. An optimum configuration of an ocean-bottom control-net unit is provided.