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.↗
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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.↗
A Lagrange-D'Alembert formulation of the equations of motion of a helicopter carrying an externally suspended load
The exact nonlinear equations of motion are derived for a helicopter with an extenal load suspended by fore and aft, rigid-link cables. Lagrange's form of D'Alembert's principle is used. Ten degrees of freedom are necessary to represent the motion of this system in an inertial reference frame: six for the helicopter relative to inertial space and four for the load relative to the helicopter.
Weber, J. M.↗
Minimum fuel trajectories for a low-thrust power-limited mission to the moon and to Lagrange points L4 and L5
Minimum fuel trajectories from a low earth parking orbit to Lagrange points L4 or L5 and to the moon are obtained for a low-thrust limited-power spacecraft, with thrust acceleration levels of the order of 0.001 G. The procedure to find a trajectory to the libration point starts from an analytical description of a slightly elliptical spiral, given by Breakwell and Rauch. The earth moon trajectory is found by matching an earth spiral to a moon spiral on the sphere of influence. Earth oblateness effect is considered.
Breakwell, John V.↗
A Lagrange multiplier based divide and conquer finite element algorithm
A novel domain decomposition method based on a hybrid variational principle is presented. Prior to any computation, a given finite element mesh is torn into a set of totally disconnected submeshes. First, an incomplete solution is computed in each subdomain. Next, the compatibility of the displacement field at the interface nodes is enforced via discrete, polynomial and/or piecewise polynomial Lagrange multipliers. In the static case, each floating subdomain induces a local singularity that is resolved very efficiently. The interface problem associated with this domain decomposition method is, in general, indefinite and of variable size. A dedicated conjugate projected gradient algorithm is developed for solving the latter problem when it is not feasible to explicitly assemble the interface operator. When implemented on local memory multiprocessors, the proposed methodology requires less interprocessor communication than the classical method of substructuring. It is also suitable for parallel/vector computers with shared memory and compares favorably with factorization based parallel direct methods.
Farhat, C.↗
On a Lagrange-Hamilton formalism describing position and momentum uncertainties
According to Heisenberg's uncertainty relation, in quantum mechanics it is not possible to determine, simultaneously, exact values for the position and the momentum of a material system. Calculating the mean value of the Hamiltonian operator with the aid of exact analytic Gaussian wave packet solutions, these uncertainties cause an energy contribution additional to the classical energy of the system. For the harmonic oscillator, e.g., this nonclassical energy represents the ground state energy. It will be shown that this additional energy contribution can be considered as a Hamiltonian function, if it is written in appropriate variables. With the help of the usual Lagrange-Hamilton formalism known from classical particle mechanics, but now considering this new Hamiltonian function, it is possible to obtain the equations of motion for position and momentum uncertainties.
Schuch, Dieter↗
Domain decomposition methods for nonconforming finite element spaces of Lagrange-type
In this article, we consider the application of three popular domain decomposition methods to Lagrange-type nonconforming finite element discretizations of scalar, self-adjoint, second order elliptic equations. The additive Schwarz method of Dryja and Widlund, the vertex space method of Smith, and the balancing method of Mandel applied to nonconforming elements are shown to converge at a rate no worse than their applications to the standard conforming piecewise linear Galerkin discretization. Essentially, the theory for the nonconforming elements is inherited from the existing theory for the conforming elements with only modest modification by constructing an isomorphism between the nonconforming finite element space and a space of continuous piecewise linear functions.
Cowsar, Lawrence C.↗
A study of angular momentum loss in binaries using the free Lagrange method
The evolution of a binary star system depends greatly on the angular momentum losses in the system brought about by gravitational radiation and mass outflow (e.g., evaporating winds and magnetic braking) from the secondary component of the binary. Using a three-dimensional hydrodynamic fluid code based on the free Lagrange method, we study the loss of specific angular momentum from a binary system due to an evaporative wind from the companion of a millisecond pulsar. We consider binaries of different mass ratios and winds of different initial velocities and in particular attempt to model the system PSR 1957+20. We are in the process of incorporating the effect of the radiation force from the pulsar and the magnetic field of the companion on the mass outflow. The latter effect would also enable us to study magnetic braking in cataclysmic variables and low-mass X-ray binaries.
Rajasekhar, A. M.↗