Research in precision integration methods Final report, 1 Apr. 1969 - 31 Mar. 1970
Methods for numerically integrating systems of coupled nonlinear differential equations
Gallaher, L. J.↗
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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Theory of radiative transfer in inhomogeneous atmospheres. II
Perturbation method developed for linearizing nonlinear singular equation for inhomogeneous stratified atmosphere H-function in theory of radiative transfer
Abhyankar, K. D.↗
Finite-element technique applied to heat conduction in solids with temperature dependent thermal conductivity
Finite element method applied to heat conduction in solids with temperature dependent thermal conductivity, using nonlinear constitutive equation for heat ABCDEFGHIABCDEFGHIABCDEFGHIABCDEFGHIABCDEFGHIABCDEFGHIABCDEFGHIABCDEFGHIABCDEFGHIABCDEFGHIABCDEFGHIABCDEFGH
Aguirre-Ramirez, G.↗
Nonlinear Vlasov plasmas - Initial value problem and response to an external field
Numerical solution of nonlinear Vlasov equation for collisionless plasma problems, discussing initial value problems, external electric fields, magnetic fields, etc
Montgomery, D.↗
Mathematical models of plasma
Nonlinear Vlasov equation treatment by Fourier- Hermite expansion techniques for plasma problems
Feix, M.↗
Analysis of a control system containing two nonlinearities
Parameter plane method of stability analysis applied to spacecraft attitude control system with two nonlinearities related by nonlinear differential equation
Seltzer, S. M.↗
Nonlinear combustion instability in liquid- propellant rocket engines
Liquid propellant rocket engine combustion instabilities, describing unsteady combustor flow by single nonlinear wave equation with stable and unstable finite amplitude limit cycles
Powell, E. A.↗
Nonlinear oscillations and stability bounds in a nuclear reactor with linear reactivity feedback Semiannual report
Nonlinear differential equations describing stability of fast nuclear reactor with incore thermionic converters and reactivity feedback
Yee, S.↗
Study of non-linear optimization techniques
Nonlinear optimization techniques in dynamic programming and solution of ordinary nonlinear differential equations by Runge-Kutta method
Shanks, E. B.↗
A study on the optimal rocket trajectory
Optimal vacuum rocket trajectories over spherical earth, deriving nonlinear differential equations for position and velocity
Burns, R. E.↗
Collisionless sheath near an electrode in the presence of a magnetic field
Magnetic field effects on collisionless plasma sheath near planar electrode, solving electric and magnetic potentials nonlinear differential equations by numerical scheme
Hassan, H. A.↗
Thermochemical nonequilibrium in an argon constricted arc plasma
Ar arc plasma thermochemical nonequilibrium, using finite difference techniques for nonlinear integrodifferential equations
Clark, K. J.↗
Numerical calculation of transonic flow about two-dimensional airfoils by relaxation procedures
Compressible transonic flow about two dimensional airfoils, developing inviscid nonlinear potential equations by relaxation procedures
Lomax, H.↗
An all digital phase locked loop for FM demodulation
Digital phase locked loop for FM signals demodulation, considering system nonlinear difference equation
Garodnick, J.↗
Integral manifolds for perturbed nonlinear systems
Bounded integral manifolds existence for perturbed system of nonlinear differential equations near critical point, periodic orbit or periodic surface
Suber, H. H.↗
Computer program for calculation of complex chemical equilibrium compositions
Computer program is described for numerical solution of chemical equilibria in complex systems by using nonlinear algebraic equations. Free-energy minimization technique is used.
Gordon, S.↗
A finite element procedure for nonlinear prebuckling and initial postbuckling analysis
A procedure cast in a form appropriate to the finite element method is presented for geometrically nonlinear prebuckling and postbuckling structural analysis, including the identification of snap-through type of buckling. The principal features of this procedure are the use of direct iteration for solution of the nonlinear algebraic equations in the prebuckling range, an interpolation scheme for determination of the initial bifurcation point, a perturbation method in definition of the load-displacement behavior through the postbuckling regime, and extrapolation in determination of the limit point for snap-through buckling. Three numerical examples are presented in illustration of the procedure and in comparison with alternative approaches.
Mau, S. T.↗
Design of minimax output feedback controller for system with parameter uncertainty
The problem of controlling a time-invariant system with parameter uncertainty is considered with incomplete state feedback. The controller is designed by minimaximizing a quadratic performance criterion and a sensitivity (or loss) criterion, involving the state of the system, the control, and the uncertainty vector. The resulting optimal controller is linear and optimal feedback gain matrix must satisfy a set of nonlinear algebraic equations. some algorithms for algebraic minimax problems are presented.
Basuthakur, S.↗