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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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All sourcesNASA NTRSDOE OSTI
NASA NTRS1974

A macroscopic plasma Lagrangian and its application to wave interactions and resonances

The derivation of a macroscopic plasma Lagrangian is considered, along with its application to the description of nonlinear three-wave interaction in a homogeneous plasma and linear resonance oscillations in a inhomogeneous plasma. One approach to obtain the Lagrangian is via the inverse problem of the calculus of variations for arbitrary first and second order quasilinear partial differential systems. Necessary and sufficient conditions for the given equations to be Euler-Lagrange equations of a Lagrangian are obtained. These conditions are then used to determine the transformations that convert some classes of non-Euler-Lagrange equations to Euler-Lagrange equation form. The Lagrangians for a linear resistive transmission line and a linear warm collisional plasma are derived as examples. Using energy considerations, the correct macroscopic plasma Lagrangian is shown to differ from the velocity-integrated low Lagrangian by a macroscopic potential energy that equals twice the particle thermal kinetic energy plus the energy lost by heat conduction.

Peng, Y. K. M.↗
NASA NTRS1976

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↗
NASA NTRS1987

Slew maneuver dynamics of the Spacecraft Control Laboratory experiment

Mathematical expressions for slew maneuver dynamics are presented. The total kinetic energy expression of the system is given as T = T(0) + T(1) + T(2), where T(0), T(1), and T(2) refer to the kinetic energies of the shuttle, the flexible beam, and the tip mass (the reflector), respectively. The specific equations for each of these are defined and integrated into the total energy expression. Using the chain rule in the Lagrange equations and an expression allowing the transformation of the orbiter angular velocity from the inertial frame to the body-fixed frame, the rotational equations are obtained. Finally, the vibration equations for the beam are derived, again using the Lagrange equations.

Kakad, Y. P.↗
NASA NTRS1984

A Lagrangian theory of the classical spinning electron

A Lagrangian is defined that governs the dynamics of a classical electron with spin, moving under the influence of electromagnetic forces. The Euler-Lagrange equations associated with this Lagrangian for space-time position x exp-alpha provide a generalization of the Lorentz force law. The remaining Euler-Lagrange equations lead directly to the (generalized) Frenkel (1926)-Thomas (1927)-BMT (1959) equations.

Nash, P. L.↗
NASA NTRS1985

Variation objective analyses for cyclone studies

The objectives were to: (1) develop an objective analysis technique that will maximize the information content of data available from diverse sources, with particular emphasis on the incorporation of observations from satellites with those from more traditional immersion techniques; and (2) to develop a diagnosis of the state of the synoptic scale atmosphere on a much finer scale over a much broader region than is presently possible to permit studies of the interactions and energy transfers between global, synoptic and regional scale atmospheric processes. The variational objective analysis model consists of the two horizontal momentum equations, the hydrostatic equation, and the integrated continuity equation for a dry hydrostatic atmosphere. Preliminary tests of the model with the SESMAE I data set are underway for 12 GMT 10 April 1979. At this stage of purpose of the analysis is not the diagnosis of atmospheric structures but rather the validation of the model. Model runs for rawinsonde data and with the precision modulus weights set to force most of the adjustment of the wind field to the mass field have produced 90 to 95 percent reductions in the imbalance of the initial data after only 4-cycles through the Euler-Lagrange equations. Sensitivity tests for linear stability of the 11 Euler-Lagrange equations that make up the VASP Model 1 indicate that there will be a lower limit to the scales of motion that can be resolved by this method. Linear stability criteria are violated where there is large horizontal wind shear near the upper tropospheric jet.

Achtemeier, G. L.↗
NASA NTRS1976

Lagrangian density for collisional plasma

For the purpose of deriving appropriate Lagrangians for plasma equations that include effects of energy loss, the paper examines the inverse problem of the calculus of variations for systems of first- and second-order quasi-linear partial differential equations. This results in convenient forms of the sufficient conditions under which the given differential equations are Euler-Lagrange equations of a Lagrangian. These conditions are then applied to determine the necessary transformation that converts equations, apparently not already in it, into Euler-Lagrange form. The appropriate Lagrangian for a warm collisional plasma is obtained, and the Lagrangian is derived for a resistive transmission line.

Peng, Y.-K. M.↗
NASA NTRS2001

Multi-Tethered Space-Based Interferometers: Particle System Model

Dynamics models are presented for a class of space-based interferometers comprised of multiple component bodies, interconnected in various arrangements, by low-mass flexible tethers of variable length. The tethered constellations are to perform coordinated rotational scanning accompanied by baseline dimensional changes, as well as spin axis realignments and spin-up/spin-down maneuvers. The mechanical idealization is a system of N point masses interconnected by massless tethers of variable length. Both extensible and inextensible tethers are considered. Expressions for system angular and linear momenta are developed. The unrestricted nonlinear motion equations are derived via Lagranges equations. Rheonomic constraints are introduced to allow prescribed motion of any degrees of freedom, and the associated physical forces are determined. The linearized equations of motion are obtained for the steady rotation of a system with extensible tethers of constant unstrained length.

Gates, Stephen S.↗
NASA NTRS2003

Using Bond Graphs for Articulated, Flexible Multi-bodies, Sensors, Actuators, and Controllers with Application to the International Space Station

Conceptually, modeling of flexible, multi-body systems involves a formulation as a set of time-dependent partial differential equations. However, for practical, engineering purposes, this modeling is usually done using the method of Finite Elements, which approximates the set of partial differential equations, thus generalizing the approach to all continuous media. This research investigates the links between the Bond Graph method and the classical methods used to develop system models and advocates the Bond Graph Methodology and current bond graph tools as alternate approaches that will lead to a quick and precise understanding of a flexible multi-body system under automatic control. For long endurance, complex spacecraft, because of articulation and mission evolution the model of the physical system may change frequently. So a method of automatic generation and regeneration of system models that does not lead to implicit equations, as does the Lagrange equation approach, is desirable. The bond graph method has been shown to be amenable to automatic generation of equations with appropriate consideration of causality. Indeed human-interactive software now exists that automatically generates both symbolic and numeric system models and evaluates causality as the user develops the model, e.g. the CAMP-G software package. In this paper the CAMP-G package is used to generate a bond graph model of the International Space Station (ISS) at an early stage in its assembly, Zvezda. The ISS is an ideal example because it is a collection of bodies that are articulated, many of which are highly flexible. Also many reaction jets are used to control translation and attitude, and many electric motors are used to articulate appendages, which consist of photovoltaic arrays and composite assemblies. The Zvezda bond graph model is compared to an existing model, which was generated by the NASA Johnson Space Center during the Verification and Analysis Cycle of Zvezda.

Montgomery, Raymond C.↗
DOE OSTI2025

Large deviations of ionic currents in dilute electrolytes

Here, we evaluate the exponentially rare fluctuations of the ionic current for a dilute electrolyte by means of macroscopic fluctuation theory. We consider the fluctuating hydrodynamics of a fluid electrolyte described by a stochastic Poisson–Nernst–Planck equation. We derive the Euler–Lagrange equations that dictate the optimal concentration profiles of ions conditioned on exhibiting a given current, whose form determines the likelihood of that current in the long-time limit. For a symmetric electrolyte under small applied voltages, number density fluctuations are small, and ionic current fluctuations are Gaussian with a variance determined by the Nernst–Einstein conductivity. Under large applied potentials, the ionic current distribution is generically non-Gaussian. Its structure is constrained thermodynamically by Gallavotti–Cohen symmetry and the thermodynamic uncertainty principle.

Farhadi, Jafar [University of California, Berkeley↗
NASA NTRS1988

A multivariate variational objective analysis-assimilation method. Part 1: Development of the basic model

The variational method of undetermined multipliers is used to derive a multivariate model for objective analysis. The model is intended for the assimilation of 3-D fields of rawinsonde height, temperature and wind, and mean level temperature observed by satellite into a dynamically consistent data set. Relative measurement errors are taken into account. The dynamic equations are the two nonlinear horizontal momentum equations, the hydrostatic equation, and an integrated continuity equation. The model Euler-Lagrange equations are eleven linear and/or nonlinear partial differential and/or algebraic equations. A cyclical solution sequence is described. Other model features include a nonlinear terrain-following vertical coordinate that eliminates truncation error in the pressure gradient terms of the horizontal momentum equations and easily accommodates satellite observed mean layer temperatures in the middle and upper troposphere. A projection of the pressure gradient onto equivalent pressure surfaces removes most of the adverse impacts of the lower coordinate surface on the variational adjustment.

Achtemeier, Gary L.↗
NASA NTRS1994

An Approach for Dynamic Grids

An approach is presented for the generation of two-dimensional, structured, dynamic grids. The grid motion may be due to the motion of the boundaries of the computational domain or to the adaptation of the grid to the transient, physical solution. A time-dependent grid is computed through the time integration of the grid speeds which are computed from a system of grid speed equations. The grid speed equations are derived from the time-differentiation of the grid equations so as to ensure that the dynamic grid maintains the desired qualities of the static grid. The grid equations are the Euler-Lagrange equations derived from a variational statement for the grid. The dynamic grid method is demonstrated for a model problem involving boundary motion, an inviscid flow in a converging-diverging nozzle during startup, and a viscous flow over a flat plate with an impinging shock wave. It is shown that the approach is more accurate for transient flows than an approach in which the grid speeds are computed using a finite difference with respect to time of the grid. However, the approach requires significantly more computational effort.

Slater, John W.↗
NASA NTRS1967

Study of dynamic response of elastic space stations

Analytical procedure and the requisite computer programs compute the dynamic responses of two large elastic space stations. The linearized equations of motion are derived from lagranges equations. Then the normal modes of free vibration of the nonrotating space station are used to define the elastic degrees of freedom.

Kamrath, P.↗
NASA NTRS1989

Connection forces in deformable multibody dynamics

In the dynamic formulation of holonomic and nonholonomic systems based on D'Alembert-Lagrange equation, the forces of constraints are maintained in the dynamic equations by introducing auxiliary variables, called Lagrange multipliers. This approach introduces a set of generalized reaction forces associated with the system generalized coordinates. Different sets of variables can be used as generalized coordinates and accordingly, the generalized reactions associated with these generalized coordinates may not be the actual reaction forces at the joints. In rigid body dynamics, the generalized reaction forces and the actual reaction forces at the joints represent equipollent systems of forces since they produce the same total forces and moments at and about any point on the rigid body. This is not, however, the case in deformable body analyses wherein the generalized reaction forces depend on the system generalized reference and elastic coordinates. In this paper, a method for determining the actual reaction forces at the joints from the generalized reaction forces in deformable multibody systems is presented.

Shabana, A. A.↗