Simplified application of Lighthill's uniformization technique using Lagrange expansion formulas.
Lighthill uniformization technique applied to singular perturbation problems using Lagrange expansion
LEADING EDGE↗
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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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A direct method for estimating Lagrange's multipliers in trajectory optimization problems.
Lagrange multipliers in two-point boundary condition problems for trajectory optimization estimated by direct method
NUMERICAL INTEGRATION↗
On an extension of the Lagrange-Laplace theory of the Moon's physical librations.
Lagrange-Laplace theory of lunar physical librations extended to include reduced estimate of mechanical ellipticity of lunar equator
LIBRATIONAL MOTION↗
Euler-Lagrange relationship for random dispersive waves
Euler-Lagrange relationship for random dispersive waves
Hoult, D. P.↗
An explicit solution for the Lagrange multipliers on the singular subarc of an optimal trajectory.
Optimal thrust programming of single stage rocket vehicle for maximum payoff at end conditions using Lagrange multipliers for singular arc
Burns, R. E.↗
Euler-Lagrange relationship for random dispersive waves Scientific report
Euler-Lagrange relationship for random dispersive waves
Hoult, D. P.↗
Recurrent nature of Lagrange multipliers for optimal low-thrust earth-Jupiter transfers.
Recurrent Lagrange multipliers for optimal low thrust earth-Jupiter transfers, using three dimensional solar system model
Fowler, W. T.↗
Optimal control problems as equivalent Lagrange problems
Transforming optical control problem into equivalent Lagrange problem in calculus of variations
Park, S. K.↗
On the equivalence of optimal control problems and the transformation of optimal control problems with compact control regions into Lagrange problems
Equivalence of optimal control problems and transformation of optimal control problems with compact control regions into Lagrange problems
Park, S. K.↗
Maximum-minimum sufficiency and Lagrange multipliers
Necessary and sufficient conditions for constrained extrema without use of Lagrange multipliers
Cliff, E. M.↗
Generalizations of Lagrange's expansion combined with Lighthill's technique for uniformizing solutions of partial differential equations
Lighthill method with Lagrange expansion for approximative solutions of partial differential equations
Martin, E. D.↗
Further results on recurrent Lagrange multipliers for the low-thrust Earth-Jupiter transfer
Recurrent Lagrange multipliers coordinate transformation for optimal low thrust Earth- Jupiter trajectories
Fowler, W. T.↗
Generalization of Lagrange's implicit function theorem to n-dimensions
Lagrange implicit functions generalization to n dimensions, developing inversion as power series
Feagin, T.↗
Analysis of complex elastic structures by a Rayleigh-Ritz component modes method using Lagrange multipliers
The free vibrations of elastic structures of arbitrary complexity were analyzed in terms of their component modes. The method was based upon the use of the normal unconstrained modes of the components in a Rayleigh-Ritz analysis. The continuity conditions were enforced by means of Lagrange Multipliers. Examples of the structures considered are: (1) beams with nonuniform properties; (2) airplane structures with high or low aspect ratio lifting surface components; (3) the oblique wing airplane; and (4) plate structures. The method was also applied to the analysis of modal damping of linear elastic structures. Convergence of the method versus the number of modes per component and/or the number of components is discussed and compared to more conventional approaches, ad-hoc methods, and experimental results.
Klein, L. R.↗
Long period coupling terms for Lagrange's equations
A generalization of that portion of the work of Berger, which deals with the long period coupling effect of certain pairs of zonal harmonics. Long period terms arising from the short short period coupling of zonal harmonics are derived for Lagrange's equations. The formulation is general so that the results are valid for any pairs of zonal harmonics. Formulas are given to generate the various functions and integrals needed for the results given. Checks have been made against the work of Kozai.
Source record↗
Lagrange duality theory for convex control problems
The Lagrange dual to a control problem is studied. The principal result based on the Hahn-Banach theorem proves that the dual problem has an optimal solution if there exists an interior point for the constraint set. A complementary slackness condition holds, if the primal problem has an optimal solution. A necessary and sufficient condition for the optimality of solutions to the primal and the dual problem is also presented.
Hager, W. W.↗
A suggested trajectory for a Venus-sun, earth-sun Lagrange points mission, Vela
The possibility is suggested of investigating the existence of small, as-yet undiscovered, asteroids orbiting in the solar system near the earth-sun or Venus-sun stable Lagrange points by means of a spacecraft which traverses these regions. The type of trajectory suggested lies in the ecliptic plane and has a period of 5/6 years and a perihelion at the Venus orbital distance. The regions in which stable orbits associated with the earth and with Venus may lie are estimated to be a thin and tadpole-shaped area extending from 35 deg to 100 deg from the planet. Crossings of the regions by the trajectory are described, and the requirements for detecting the presence of 1 km sized asteroids are presented and shown to be attainable.
Bender, D. F.↗
Power system design optimization using Lagrange multiplier techniques
An optimization technique using the Lagrange Multiplier Method is proposed to facilitate design of switching power converter systems. The essence of the optimization is to identify the optimal battery voltage level and switching frequency along with the detailed converter design so that the total system weight including the battery and the packaged converter is minimized, and concurrently all specified power circuit performances are satisfied.
Yu, Y.↗