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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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NASA NTRS1975

On redundant variables in Lagrangian mechanics, with applications to perturbation theory and KS regularization

It is shown that it is possible to make a change of variables in a Lagrangian in such a way that the number of variables is increased. The Euler-Lagrange equations in the redundant variables are obtained in the standard way (without the use of Lagrange multipliers). These equations are not independent but they are all valid and consistent. In some cases they are simpler than if the minimum number of variables are used. The redundant variables are supposed to be related to each other by several constraints (not necessarily holonomic), but these constraints are not used in the derivation of the equations of motion. The method is illustrated with the well known Kustaanheimo-Stiefel regularization. Some interesting applications to perturbation theory are also described.

Broucke, R.↗
NASA NTRS1974

Program manual for HILTOP, a heliocentric interplanetary low thrust trajectory optimization program. Part 1: User's guide

A performance-analysis computer program, that was developed explicitly to generate optimum electric propulsion trajectory data for missions of interest in the exploration of the solar system is presented. The program was primarily designed to evaluate the performance capabilities of electric propulsion systems, and in the simulation of a wide variety of interplanetary missions. A numerical integration of the two-body, three-dimensional equations of motion and the Euler-Lagrange equations was used in the program. Transversality conditions which permit the rapid generation of converged maximum-payload trajectory data, and the optimization of numerous other performance indices for which no transversality conditions exist are included. The ability to simulate constrained optimum solutions, including trajectories having specified propulsion time and constant thrust cone angle, is also in the program. The program was designed to handle multiple-target missions with various types of encounters, such as rendezvous, stopover, orbital capture, and flyby. Performance requirements for a variety of launch vehicles can be determined.

Mann, F. I.↗
NASA NTRS1974

Microscopic plasma Hamiltonian

A Hamiltonian for the microscopic plasma model is derived from the Low Lagrangian after the dual roles of the generalized variables are taken into account. The resulting Hamilton equations are shown to agree with the Euler-Lagrange equations of the Low Lagrangian.

Peng, Y.-K. M.↗
NASA NTRS1980

Modal methods in optimal control synthesis

Efficient algorithms for solving linear smoother-follower problems with quadratic criteria are presented. For time-invariant systems, the algorithm consists of one backward integration of a linear vector equation and one forward integration of another linear vector equation. Furthermore, the backward and forward Riccati matrices can be expressed in terms of the eigenvalues and eigenvectors of the Euler-Lagrange equations. Hence, the gains of the forward and backward Kalman-Bucy filters and of the optimal state-feedback regulator can be determined without integration of matrix Riccati equations. A computer program has been developed, based on this method of determining the gains, to synthesize the optimal time-invariant compensator in the presence of random disturbance inputs and random measurement errors. The program also computes the rms state and control variables of the optimal closed-loop system.

Bryson, A. E., Jr.↗
NASA NTRS1991

A Variational Formalism for the Radiative Transfer Equation and a Geostrophic, Hydrostatic Atmosphere: Prelude to Model 3

The second step in development of MODEL III is summarized. It combines the four radiative transfer equations of the first step with the equations for a geostrophic and hydrostatic atmosphere. This step is intended to bring radiance into a three dimensional balance with wind, height, and temperature. The use of the geostrophic approximation in place of the full set of primitive equations allows for an easier evaluation of how the inclusion of the radiative transfer equation increases the complexity of the variational equations. Seven different variational formulations were developed for geostrophic, hydrostatic, and radiative transfer equations. The first derivation was too complex to yield solutions that were physically meaningful. For the remaining six derivations, the variational method gave the same physical interpretation (the observed brightness temperatures could provide no meaningful input to a geostrophic, hydrostatic balance) at least through the problem solving methodology used in these studies. The variational method is presented and the Euler-Lagrange equations rederived for the geostrophic, hydrostatic, and radiative transfer equations.

Achtemeier, Gary L.↗
NASA NTRS1972

Earth zonal harmonics from rapid numerical analysis of long satellite arcs

A zonal geopotential is presented to degree 21 from evaluation of mean elements for 21 satellites including 2 of low inclination. Each satellite is represented by an arc of at least one apsidal rotation. The lengths range from 200 to 800 days. Differential correction of the initial elements in all of the arcs, together with radiation pressure and atmospheric drag coefficients, was accomplished simultaneously with the correction for the zonal harmonics. The satellite orbits and their variations are generated by numerical integration of the Lagrange equations for mean elements. Disturbances due to precession and nutation of the earth's pole, atmospheric drag, radiation pressure and luni-solar gravity are added at from 1- to 8-day intervals in the integrated orbits. The results agree well with recent solutions from other authors using different methods and different satellite sets.

Wagner, C. A.↗
NASA NTRS1972

Canonical fluid thermodynamics

The space-time integral of the thermodynamic pressure plays the role of the thermodynamic potential for compressible, adiabatic flow in the sense that the pressure integral for stable flow is less than for all slightly different flows. This stability criterion can be converted into a variational minimum principle by requiring the molar free-enthalpy and the temperature, which are the arguments of the pressure function, to be generalized velocities, that is, the proper-time derivatives of scalar spare-time functions which are generalized coordinates in the canonical formalism. In a fluid context, proper-time differentiation must be expressed in terms of three independent quantities that specify the fluid velocity. This can be done in several ways, all of which lead to different variants (canonical transformations) of the same constraint-free action integral whose Euler-Lagrange equations are just the well-known equations of motion for adiabatic compressible flow.

Schmid, L. A.↗
NASA NTRS1972

Cable Connected Spinning Spacecraft, 1. the Canonical Equations, 2. Urban Mass Transportation, 3

Work on the dynamics of cable-connected spinning spacecraft was completed by formulating the equations of motion by both the canonical equations and Lagrange's equations and programming them for numerical solution on a digital computer. These energy-based formulations will permit future addition of the effect of cable mass. Comparative runs indicate that the canonical formulation requires less computer time. Available literature on urban mass transportation was surveyed. Areas of the private rapid transit concept of urban transportation are also studied.

Sitchin, A.↗
NASA NTRS1973

Zonal gravity harmonics from long satellite arcs by a seminumeric method.

A zonal geopotential is presented to degree 21 from evaluation of mean elements for 21 satellites, including two of low (less than 20 deg) inclination. Each satellite is represented by an arc of at least one apsidal rotation. The lengths range from 50 to 660 days. Differential correction of the initial elements in all of the arcs, together with radiation pressure and atmospheric drag coefficients, is accomplished simultaneously with the correction for the zonal harmonics. The satellite orbits and their variations are generated by numerical integration of the Lagrange equations for mean elements. Disturbances due to precession and nutation, atmospheric drag, radiation pressure, and lunisolar gravity are added at 1- to 8-day intervals in the integrated orbits.

Wagner, C. A.↗
NASA NTRS1973

Classical trajectory study of the K + CH3I reaction

Potential surfaces for the system K+IR were considered, taking into account a covalent surface, an ionic surface, the overall potential, and a comparison of a modified Bunker-Blais and a hybrid covalent-ionic potential of the electron-jump type. The Lagrange equations were solved as a system of second-order differential equations. The impact parameter, angular, and energy dependences of the product distributions for the nonreactive, reactive, and dissociative scattering were studied.

Labudde, R. A.↗
NASA NTRS1983

Macroscopic Lagrangian description of warm plasmas. I Formulation of the Lagrangian

A macroscopic Lagrangian is derived which includes a pressure tensor, heat conduction, and elastic collisions. Its Euler-Lagrange equations are shown to be the Maxwell equations and the macroscopic force law. The corresponding Hamiltonian is derived, and Hamilton's canonical equations are also demonstrated to lead to the Maxwell equations and the macroscopic force law. The treatment is facilitated by working in a mixture of Eulerian coordinates (for the fields) and Lagrangian coordinates (for the particle motions), and the introduction of a macroscopic potential expressed in terms of the plasma thermal energy and the energy losses by heat conduction.

Peng, Y.-K. M.↗
NASA NTRS1988

Minimum dissipation rates in magnetohydrodynamics

Minimum dissipation rate states are explored for a current-carrying channel of magnetofluid, supported by a dc magnetic field and driven by an applied electric field. The minimization is carried out subject to the constraints of constant axial (toroidal) magnetic flux and constant time-averaged rate of supply of magnetic helicity. The solutions of the resulting Euler-Lagrange equations are sensitive to boundary conditions on the current density j. One set of boundary conditions on j leads to the same consequences as Taylor's 'minimum-energy' theory. A different set leads to significantly different consequences, including a departure from the 'force-free' magnetic profile and a toroidal component of current density that does not reverse at the wall when the toroidal magnetic field reverses.

Montgomery, David↗
NASA NTRS1990

Energy stability of thermocapillary convection in a model of the float-zone crystal-growth process

Energy stability theory has been applied to a basic state of thermocapillary convection occurring in a cylindrical half-zone of finite length to determine conditions under which the flow will be stable. Because of the finite length of the zone, the basic state must be determined numerically. Instead of obtaining stability criteria by solving the related Euler-Lagrange equations, the variational problem is attacked directly by discretization of the integrals in the energy identity using finite differences. Results of the analysis are values of the Marangoni number below which axisymmetric disturbances to the basic state will decay, for various values of the other parameters governing the problem.

Shen, Y.↗
NASA NTRS1991

Methods of applied dynamics

The monograph was prepared to give the practicing engineer a clear understanding of dynamics with special consideration given to the dynamic analysis of aerospace systems. It is conceived to be both a desk-top reference and a refresher for aerospace engineers in government and industry. It could also be used as a supplement to standard texts for in-house training courses on the subject. Beginning with the basic concepts of kinematics and dynamics, the discussion proceeds to treat the dynamics of a system of particles. Both classical and modern formulations of the Lagrange equations, including constraints, are discussed and applied to the dynamic modeling of aerospace structures using the modal synthesis technique.

Rheinfurth, M. H.↗