Minimum fuel attitude control of a non-linear satellite system
Nonlinear satellite system attitude control for minimum fuel consumption, deriving linear programming algorithm based on optimal control theory
Wolske, G. D.↗
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Electronic switching circuit uses complementary non-linear components
Inherent switching properties of saturable inductors and storage diodes are combined to perform large variety of electronic functions, such as pulse shaping, gating, and multiplexing. Passive elements replace active switching devices in generation of complex waveforms.
Zucker, O. S.↗
Convergence of step-by-step methods for non-linear integro-differential equations.
The theory of consistent step-by-step methods for solving Volterra integral equations is extended to nonsingular Volterra integro-differential equations. It is shown that standard step-by-step algorithms for these more general equations are convergent. Several numerical examples are included.
Mocarsky, W. L.↗
Aperiodic behaviour of a non-linear oscillator.
The aperiodic behavior of the solution of the equation of motion derived previously (1966) when considering a model thermomechanical oscillator is examined. Periodic solutions of this equation are studied numerically and analytically. Conditions for the instability of the solutions are determined. This instability seems to be the cause of the observed aperiodicity.
Baker, N. H.↗
A study and classification of non-linear high frequency ionospheric instabilities by coupled mode theory.
Two basic high-frequency ionospheric instabilities are discussed - i.e., the three-wave parametric interaction, and the oscillating two-stream instability. In the parametric instability, the ion-acoustic wave has a complex frequency, whereas in the oscillating two-stream instability the ion-acoustic frequency is purely imaginary. The parametric instability is shown to be the only one whose threshold depends on the ion collision frequency. A coupled-mode theory is proposed which permits study and classification of high-frequency instabilities on a unified basis.
Harker, K. J.↗
Dynamic response analysis of geometrically non-linear structures subjected to high impact.
Description of an efficient digital computer method for the determination of the propagation of elastic stresses and deformations in certain geometrically nonlinear structures subjected to high impact loading. The finite-element matrix displacement approach utilizing curved quadrilateral shell elements in conjunction with a nodewise predictor-corrector method employing Runge-Kutta extrapolation techniques has been adopted for the present solution. The related computer program written in FORTRAN V for the UNIVAC 1108 computer has proved to be effective for the solution of a range of practical problems including rectangular and cylindrical panels. Numerical results are presented for a relevant structure, the cell container, and the negative electrode of an impact-resistant battery subjected to high impact, simulating its free landing on a planetary surface.
Gupta, K. K.↗
A non-linear dynamic lumped-parameter model of a rectangular plate.
A lumped-parameter model of a rectangular plate is developed by assuming fundamental mode solutions and using Hamilton's Principle and the Euler equations to set up the differential equation of motion for the system. The plate theory used may be described as the dynamic analogue of the von Karman large-deflection theory. Four sets of symmetrical boundary conditions are considered with the restriction of uniform pressure dynamic loads. The model takes the form of a mass on a cubic-hardening spring with each term defined by algebraic expressions of the plate parameters. The results for some specific problems are compared with two previous solutions. This method is less accurate but simpler to develop and apply.
Bayles, D. J.↗
Necessary conditions for optimality in a general class of non-linear mixed boundary value control problems.
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Bailey, J. E.↗
Full non-linear treatment of the global thermospheric wind system. Part 2: Results and comparison with observations
The inclusion effects of the nonlinear parts of the convective derivative on the resulting wind pattern are considered. A comparison is made with earlier theoretical work and with winds deduced from observations.
Blum, P. W.↗
Non-linear flap-lag dynamics of hingeless helicopter blades in hover and in forward flight.
The aeroelastic instability of the coupled nonlinear flap-lag motion of a torsionally rigid helicopter blade is treated by using the perturbation method in multiple time scales. The nonlinearities present in the equations are those arising from the inclusion of moderately large deflections in the inertia and aerodynamic loading terms. The stability boundaries, amplitudes of nonlinear response, and conditions for existence of limit cycles are obtained analytically. Thus the different roles played by the forcing, parametric excitation, and nonlinear coupling in affecting the solution can be easily identified. Numerical results illustrating the behavior of the blade are presented.
Friedmann, P.↗
L/superscript-p/ stability /p ranging from 1 to infinity/ of multivariable non-linear time-varying feedback systems that are open-loop unstable
The loop transformation technique (Sandberg, 1965; Zames, 1966, Willems, 1971), and the fixed point theorem (Schwartz, 1970) are used to derive the L(superscript-p) stability for a class of multivariable nonlinear time-varying feedback systems which are open-loop unstable. The application of the fixed point theorem in L(superscript-p) shows that the nonlinear feedback system has one and only one solution for any pair of inputs in L(superscript-p), that the solutions are continuously dependent on the inputs, and that the closed loop system is L(superscript-p)-stable for any p ranging from 1 to infinity.
Callier, F. M.↗
Synthesis of a non-linear feedback system with significant plant-ignorance for prescribed system tolerances
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Krishnan, K. R.↗
Phase-bunching and other non-linear processes occurring in gyroresonant wave-particle interactions
Consideration of the movement of individual electrons in a magnetized plasma in which a monochromatic wave is propagating in the whistler mode. Simple expressions are derived which give the displacement of the electrons as a function of time, the phase angle that their velocity vector makes with the magnetic component of the wave, their pitch angle, and energy changes. A useful formula is obtained which gives the velocity range over which particles remain trapped inside the wave, as a function of the wave intensity and of the initial phase angle of the particle. It is shown that even strictly resonant particles can escape from the wave when their initial phase angle is very small. From the derived expressions, it is possible to compute the phase-bunching effect which occurs approximately at one trapping wavelength behind the leading edge of the interaction region.
Gendrin, R.↗
Non-linear wave propagation in acoustically lined circular ducts
An analysis is presented of the nonlinear effects of the gas motion as well as of the acoustic lining material on the transmission and attenuation of sound in a circular duct with a uniform cross-section and no mean flow. The acoustic material is characterized by an empirical, nonlinear impedance in which the instantaneous resistance is a nonlinear function of both the frequency and the acoustic velocity. The results show that there exist frequency bandwidths around the resonant frequencies in which the nonlinearity decreases the attenuation rate, and outside which the nonlinearity increases the attenuation rate, in qualitative agreement with experimental observations. Moreover, the effect of the gas nonlinearity increases with increasing sound frequency, whereas the effect of the material nonlinearity decreases with increasing sound frequency.
Nayfeh, A. H.↗
Full non-linear treatment of the global thermospheric wind system. I - Mathematical method and analysis of forces. II - Results and comparison with observations
The equations of horizontal motion of the neutral atmosphere between 120 and 500 km are integrated with the inclusion of all nonlinear terms of the convective derivative and the viscous forces due to vertical and horizontal velocity gradients. Empirical models of the distribution of neutral and charged particles are assumed to be known. The model of velocities developed is a steady state model. In Part I the mathematical method used in the integration of the Navier-Stokes equations is described and the various forces are analyzed. Results of the method given in Part I are presented with comparison with previous calculations and observations of upper atmospheric winds. Conclusions are that nonlinear effects are only significant in the equatorial region, especially at solstice conditions and that nonlinear effects do not produce any superrotation.
Blum, P. W.↗
Non-linear resonances in the forced responses of plates. I - Symmetric responses of circular plates
The dynamic analogue of the von Karman equations is used to study the symmetric response of a circular plate to a harmonic excitation when the frequency of the excitation is near one of the natural frequencies. It is shown that, in general, when there is no internal resonance (i.e., the natural frequencies are not commensurable), only the mode having a frequency near that of the excitation is strongly excited (i.e., is needed to represent the response in the first approximation). A clamped, circular plate is used as a numerical example to show that, when there is an internal resonance, more than one of the modes involved in this resonance can be strongly excited; moreover, when more than one mode is strongly excited, the lower modes can dominate the response, even when the frequency of the excitation is near that of the highest mode. This possibility was not revealed by any of the earlier studies which were based on the same governing equations.
Sridhar, S.↗
The calculation of steady non-linear transonic flow over finite wings with linear theory aerodynamics
The feasibility of calculating steady mean flow solutions for nonlinear transonic flow over finite wings with a linear theory aerodynamic computer program is studied. The methodology is based on independent solutions for upper and lower surface pressures that are coupled through the external flow fields. Two approaches for coupling the solutions are investigated which include the diaphragm and the edge singularity method. The final method is a combination of both where a line source along the wing leading edge is used to account for blunt nose airfoil effects; and the upper and lower surface flow fields are coupled through a diaphragm in the plane of the wing. An iterative solution is used to arrive at the nonuniform flow solution for both nonlifting and lifting cases. Final results for a swept tapered wing in subcritical flow show that the method converges in three iterations and gives excellent agreement with experiment at alpha = 0 deg and 2 deg. Recommendations are made for development of a procedure for routine application.
Cunningham, A. M., Jr.↗
Transfer function verification and block diagram simplification of a very high-order distributed pole closed-loop servo by means of non-linear time-response simulation
Linear frequency domain methods are inadequate in analyzing the 1975 Viking Orbiter (VO75) digital tape recorder servo due to dominant nonlinear effects such as servo signal limiting, unidirectional servo control, and static/dynamic Coulomb friction. The frequency loop (speed control) servo of the VO75 tape recorder is used to illustrate the analytical tools and methodology of system redundancy elimination and high order transfer function verification. The paper compares time-domain performance parameters derived from a series of nonlinear time responses with the available experimental data in order to select the best possible analytical transfer function representation of the tape transport (mechanical segment of the tape recorder) from several possible candidates. The study also shows how an analytical time-response simulation taking into account most system nonlinearities can pinpoint system redundancy and overdesign stemming from a strictly empirical design approach. System order reduction is achieved through truncation of individual transfer functions and elimination of redundant blocks.
Mukhopadhyay, A. K.↗