Ion motion in electrostatic dipole fields
Ion motion in field of fixed point electric dipole
Chandrasekharan, T.↗
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Motion under a periodic cubic force.
Periodic cubic differential equation of motion solved with special reference to location of fixed points and stability of solutions
Bartlett, J. H.↗
Admissibility and nonlinear Volterra integral equations
Solutions behavior of nonlinear system of linear Volterra integral equations, discussing applicability of standard fixed point theorems
Miller, R. K.↗
Calculation of free-fall trajectories using numerical optimization methods.
An important problem in space flight is the calculation of trajectories for nonthrusting vehicles between fixed points in a given time. A new procedure based on Hamilton's principle for solving such two-point boundary-value problems is presented. It employs numerical optimization methods to perform the extremization required by Hamilton's principle. This procedure is applied to the calculation of an Earth-Moon trajectory. The results show that the initial guesses required to obtain an iteration procedure which converges are not critical and that convergence can be obtained to any predetermined degree of accuracy.
Hull, D. G.↗
Digital random-number generator
For binary digit array of N bits, use N noise sources to feed N nonlinear operators; each flip-flop in digit array is set by nonlinear operator to reflect whether amplitude of generator which feeds it is above or below mean value of generated noise. Fixed-point uniform distribution random number generation method can also be used to generate random numbers with other than uniform distribution.
Brocker, D. H.↗
Semilinear (topological) spaces and applications
Semivector spaces are defined and some of their algebraic aspects are developed including some structure theory. These spaces are then topologized to obtain semilinear topological spaces for which a hierarchy of local convexity axioms is identified. A number of fixed point and minmax theorems for spaces with various local convexity properties are established. The spaces of concern arise naturally as various hyperspaces of linear and semilinear (topological) spaces. It is indicated briefly how all this can be applied in socio-economic analysis and optimization.
Prakash, P.↗
New hardware realizations of nonrecursive digital filters.
Analysis of the bit-level operations involved in the convolution realizing a nonrecursive digital filter leads to hardware designs of digital filters based on the operation of counting. Two distinct designs are outlined: the first one is capable of very high speed but is rather expensive; the second is quite slow but has the advantages of low cost and high flexibility. The basic designs considered utilize fixed-point representation for the data and filter coefficients. Variants allowing floating-point representation of the coefficients are also described.
Zohar, S.↗
Lp-stability (1 less than or equal to p less than or equal to infinity) of multivariable nonlinear time-varying feedback systems that are open-loop unstable
A class of multivariable, nonlinear time-varying feedback systems with an unstable convolution subsystem as feedforward and a time-varying nonlinear gain as feedback was considered. The impulse response of the convolution subsystem is the sum of a finite number of increasing exponentials multiplied by nonnegative powers of the time t, a term that is absolutely integrable and an infinite series of delayed impulses. The main result is a theorem. It essentially states that if the unstable convolution subsystem can be stabilized by a constant feedback gain F and if incremental gain of the difference between the nonlinear gain function and F is sufficiently small, then the nonlinear system is L(p)-stable for any p between one and infinity. Furthermore, the solutions of the nonlinear system depend continuously on the inputs in any L(p)-norm. The fixed point theorem is crucial in deriving the above theorem.
Callier, F. M.↗
Implementation of digital filters for minimum quantization errors
In this paper a technique is developed for choosing programing forms and bit configurations for digital filters that minimize the quantization errors. The technique applies to digital filters operating in fixed-point arithmetic in either open-loop or closed-loop systems, and is implemented by a digital computer program that is based on a digital simulation of the system. As an output the program gives the programing form required for minimum quantization errors, the total bit configuration required in the filter, and the location of the binary decimal point at each quantizer within the filter.
Phillips, C. L.↗
Ultrasonic detection of flaws in large structural areas
System's transducer consists of three piezoelectric elements that produce relatively-wide ultrasonic beam which covers significantly larger area and can monitor from a fixed point.
Sugg, F. E.↗
Second generation timing system for ranging experiment Apollo lunar laser
The status of the timing electronics for the lunar laser ranging station in Hawaii is discussed. The aim of the experiment is to measure, with high accuracy, the distance from a fixed point on earth to a retroreflector array which was placed on the lunar surface. The operating procedure for conducting the experiment is described. The components of the system are analyzed to show the effectiveness and accuracy of the facility.
Currie, D. G.↗
Numerical study of sound propagation in a jet flow
An improved computer oriented solution method for problems involving the propagation of sound through a nonuniform jet flow is developed. The method seeks to optimize the use of computer resources such as core storage space and central memory time. Complete formulation details are presented for a jet flow model consisting of a fixed point source on the jet center line in the potential core.
Padula, S. L.↗
An improved version of the table look-up algorithm for pattern recognition
The table look-up approach to pattern recognition has been used for 3 years at several research centers in a variety of applications. A new version has been developed which is faster, requires significantly less core memory, and retains full precision of the input data. The new version can be used on low-cost minicomputers having 32K words (16 bits each) of core memory and fixed-point arithmetic; no special-purpose hardware is required. An initial FORTRAN version of this system can classify an ERTS computer-compatible tape into 24 classes in less than 15 minutes.
Eppler, W. G.↗
Measuring mandibular motions
Mandibular motion along three axes is measured by three motion transducers on floating yoke that rests against mandible. System includes electronics to provide variety of outputs for data display and processing. Head frame is strapped to test subject's skull to provide fixed point of reference for transducers.
Dimeff, J.↗
Multidimensional stochastic approximation using locally contractive functions
A Robbins-Monro type multidimensional stochastic approximation algorithm which converges in mean square and with probability one to the fixed point of a locally contractive regression function is developed. The algorithm is applied to obtain maximum likelihood estimates of the parameters for a mixture of multivariate normal distributions.
Lawton, W. M.↗
Introduction to the restricted Jupiter orbiter problem
We consider a restricted six-body problem. The Galilean satellites' orbits are circular and coplanar; Io, Europa, and Ganymede are in exact resonance; their mean longitudes obey the Laplace relation. We seek periodic orbits which avoid close approaches to any satellite; such orbits are of interest for mission planning. They are approximated as fixed points of sets of variational equations associated with time-averaged disturbing functions. Stability of the solutions is also determined. The orbits of greatest interest are: planar - twice Callisto's period, eccentricity less than or equal to 0.6; planar - four times Callisto's period, eccentricity less than or equal to 0.75; slightly inclined - twice Callisto's period, eccentricity arbitrary; and planar - 4/5 or 5/4 Europa's period.
Heppenheimer, T. A.↗
Periodic motion in a class of nth-order autonomous differential equations
Sufficient conditions are obtained for the existence of periodic motion in a class of autonomous nonlinear differential equations of order greater than two. The approach is based on the decomposition of an equation into a linear and a nonlinear part. The analysis relies on some basic ideas from linear analysis and geometry. Sufficient conditions for a periodic solution are derived by means of a general topological principle referred to as the torus principle. The existence of a periodic solution is concluded by an appropriate use of the Brouwer fixed-point theorem.
Williamson, D.↗
Compatibility check of measured aircraft responses using kinematic equations and extended Kalman filter
An extended Kalman filter smoother and a fixed point smoother were used for estimation of the state variables in the six degree of freedom kinematic equations relating measured aircraft responses and for estimation of unknown constant bias and scale factor errors in measured data. The computing algorithm includes an analysis of residuals which can improve the filter performance and provide estimates of measurement noise characteristics for some aircraft output variables. The technique developed was demonstrated using simulated and real flight test data. Improved accuracy of measured data was obtained when the data were corrected for estimated bias errors.
Klein, V.↗