A Third-order and a Fourth-order Iteration Process for Nonlinear Equations
Convergence proof and procedure for third-order and fourth-order iteration process for nonlinear equations - Newton-Raphson second-order iteration
NEWTON-RAPHSON METHOD↗
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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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Newton's method and the optimization of nonlinear systems
Newton-Raphson method applied to solution of boundary value problems in trajectory optimization
TRAJECTORY OPTIMIZATION↗
Two-point boundary-value-problem techniques.
Newton-Raphson method generalized for solution of two-point boundary value problems of nonlinear optimal control theory for digital solution
DIGITAL COMPUTER↗
Computer program reduces calculation time of normal response functions
FORTRAN 2 computer program rapidly calculates parameters of maximum likelihood estimates from sensitivity experiment data populations. The program uses the Newton-Raphson iterative procedure to calculate the mean and standard deviation of portions of the cumulative normal response function.
Alexander, M. J.↗
Computer program for network synthesis by frequency response fit
Computer program synthesizes a passive network by minimizing the difference in desired and actual frequency response. The program solves for the critical points of the error function /weighted least squares fit between calculated and desired frequency response/ by the multivariable Newton-Raphson method with components constrained to an admissible region.
Green, S.↗
Computer program provides steady state analysis for liquid propellant propulsion systems
Computer program uses Bernoullis formula and Newton-Raphson method to provide steady state fluid flow analysis of line pressure drop in a system with six outlets for each of two main storage tanks. Program flexibility arises in the ease with which changes in the fluid line geometry can be made.
Clark, R. L.↗
Program computes equilibrium normal shock and stagnation point solutions for arbitrary gas mixtures
Program computes solutions for flow parameters in arbitrary gas mixtures behind a normal and a reflected normal shock, for in-flight and shock-tube stagnation conditions. Equilibrium flow calculations are made by a free-energy minimization technique coupled with the steady-flow conservation equations and a modified Newton-Raphson iterative scheme.
Callis, L. B.↗
Computer program offers new method for constructing periodic orbits in nonlinear dynamical systems
Computer program uses an iterative method to construct precisely periodic orbits which dynamically approximate solutions that converge to precise dynamical solutions in the limit of the sequence. The method used is a modification of the generalized Newton-Raphson algorithm used in analyzing two point boundary problems.
Bennett, A. G.↗
A numerical solution of Kepler's problem in universal variables
Quadratic Newton-Raphson iteration techniques for numerical solutions of Keplers universal transcendental equation
Blanchard, R. C.↗
Extension of the finite-difference Newton- Raphson algorithm to the simultaneous optimization of trajectories and associated parameters.
Finite difference Newton-Raphson algorithm extension to solve variational equations for simultaneous optimization of trajectories and associated parameters
Van Dine, C. P.↗
An algorithm for the optimization of trajectories with associated parameters.
Finite difference Newton-Raphson algorithm extension to solve variational equations for simultaneous optimization of trajectories and associated parameters
Van Dine, C. P.↗
Optimization of control systems with discontinuities and terminal constraints.
Newton-Raphson function space algorithm for optimizing control systems with discontinuities and terminal constraints, discussing spacecraft examples
Dyer, P.↗
Optimization of control systems with discontinuities and terminal constraints.
Optimal control for systems with discontinuities and terminal constraints using Newton-Raphson algorithm /successive sweep method/
Dyer, P.↗
A nonsimilar solution for laminar and turbulent boundary layer flows including entropy layers and transverse curvature Final report
Mathematical model of nonsimilar laminar or turbulent boundary layer, including entropy layer and turbulence effects, solved by Newton-Raphson iteration
Grose, R. D.↗
Thrusting trajectory minimization program for orbital transfer maneuvers
Computer program for transfer orbit trajectory optimization based on Lagrange multipliers, Newton-Raphson method, and power series
Green, R. N.↗
Geometrically nonlinear structural analysis by direct stiffness method
Modified Newton-Raphson stiffness matrices and initial value formulations to geometrically nonlinear structural analysis for beam and plane stress triangular elements
Haisler, W. E.↗
An analysis and comparison of several trajectory optimization methods
The sensitivities of the convergence characteristics of the methods to initially assumed parameters and trial solution, convergence times, computer logic, and storage requirements are discussed. Numerical comparison of the convergence characteristics is made by considering a minimum time, low thrust, Earth-Mars transfer trajectory. A modified quasi-linearization method reduces convergence time by approximately 70% when compared with the generalized Newton-Raphson method and allows the terminal boundary to be specified by a general function of the problem variables. A uniquely specified and easily determined, time dependent weighting matrix for the gradient techniques accelerates the shaping of the optimal control program and improves the convergence characteristics during the terminal iterations. Convergence envelopes, indicating how sensitive the convergence characteristics are to initially assumed parameters, are plotted for the perturbation and quasi-linearization methods. Several iteration schemes are proposed which increase the size of the convergence envelopes and decrease the sensitivity of the method to initially assumed parameters.
Lewallen, J. M.↗
Analysis of an arched outer-race ball bearing considering centrifugal forces
A Newton-Raphson method of iteration was used in evaluating the radial and axial projection of the distance between the ball center and the outer raceway groove curvature center (V and W). Fatigue life evaluations were made. The similar analysis of a conventional bearing can be directly obtained from the arched bearing analysis by simply letting the amount of arching be zero (g = 0) and not considering equations related to the unloaded half of the outer race. The analysis was applied to a 150-mm angular contact ball bearing. Results for life, contact loads, and angles are shown for a conventional bearing (g = 0) and two arched bearings (g = 0.127 mm (0.005 in.), and 0.254 mm (0.010 in.)). The results indicate that an arched bearing is highly desirable for high speed applications. In particular, for a DN value of 3 million (20,000 rpm) and an applied axial load of 4448 N (1000 lb), an arched bearing shows an improvement in life of 306 percent over that of a conventional bearing. At 4.2 million DN (28,000 rpm), the corresponding improvement is 340 percent. It was also found for low speeds, the arched bearing does not offer the advantages that it does for high speed applications.
Hamrock, B. J.↗