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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 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 NTRS1994

Diagonalized Lagrangian Robot Dynamics

A diagonal equation for robot dynamics is developed by combining recent mass matrix factorization results with classical Lagrangian mechanics.

working joint moments total joint rotational rates↗
NASA NTRS1987

Nonlinear simulation of a flexible aircraft in maneuvering flight

A mathematical model integrating nonlinear rigid-body flight mechanics and linear aeroelastic dynamics is examined; the equations of motion for an elastic aircraft in accelerated flight are developed using Lagrangian mechanics. This approach is used to construct a simulation model of an F/A-18 (configured with tip missiles) which includes angular/elastic inertial coupling (IC). In general, the elastic modes significantly affected by IC were aerodynamically decoupled from the rest of the model. The affected modes were those which induced changes in total aircraft mass distribution. The elastic effect is noticeable if deformation-induced mass distribution changes are significant with respect to modal mass and modal frequencies. A modal parameter is presented which characterizes the level of IC between elastic momentum and rigid-body angular momentum.

Buttrill, Carey S.↗
NASA NTRS2014

Simulations of NOx Emissions from Low Emissions Discrete Jet Injector Combustor Tests

An experimental and computational study was conducted to evaluate the performance and emissions characteristics of a candidate Lean Direct Injection (LDI) combustor configuration with a mix of simplex and airblast injectors. The National Combustion Code (NCC) was used to predict the experimentally measured EINOx emissions for test conditions representing low power, medium power, and high-power engine cycle conditions. Of the six cases modeled with the NCC using a reduced-kinetics finite-rate mechanism and lagrangian spray modeling, reasonable predictions of combustor exit temperature and EINOx were obtained at two high-power cycle conditions.

Ajmani, Kumud↗
NASA NTRS1981

Simplified robot arm dynamics for control

A brief summary and evaluation is presented on the use of symbolic state equation techniques in order to represent robot arm dynamics with sufficient accuracy for controlling arm motion. The use of homogeneous transformations and the Lagrangian formulation of mechanics offers a convenient frame for the derivation, analysis and simplification of complex robot dynamics equations. It is pointed out that simplified state equations can represent robot arm dynamics with good accuracy.

Bejczy, A. K.↗
NASA NTRS1986

Computational Simplification of Robot-Arm Dynamics

Report presents two general methods for reducing mathematical complexities of state equations of robot-arm dynamics. Robot arms contain both rotary and linear joints. Both methods start with homogenous coordinates and Lagrangian formulation of mechanics briefly summarized in report. First method uses matrix-analysis techniques; second, vector-analysis techniques. Vector-analysis method includes new differential-vector representation of centripetal and Coriolis forces.

Bejczy, A. K.↗
NASA NTRS1996

Classical-Quantum Correspondence by Means of Probability Densities

Within the frame of the recently introduced phase space representation of non relativistic quantum mechanics, we propose a Lagrangian from which the phase space Schrodinger equation can be derived. From that Lagrangian, the associated conservation equations, according to Noether's theorem, are obtained. This shows that one can analyze quantum systems completely in phase space as it is done in coordinate space, without additional complications.

Vegas, Gabino Torres↗
NASA NTRS1999

Acoustic Energy Estimates in Inhomogeneous Moving Media

In ducted fan engine noise research, there is a need for defining a simple and easy to use acoustic energy conservation law to help in quantification of noise control techniques. There is a well known conservation law relating acoustic energy and acoustic energy flux in the case of an isentropic irrotational flow. Several different approaches have been taken to generalize this conservation law. For example, Morfey finds an identity by separating out the irrotational part of the perturbed flow. Myers is able to find a series of indentities by observing an algebraic relationship between the basic conservation of energy equation for a background flow and the underlying equations of motion. In an approximate sense, this algebraic relationship is preserved under perturbation. A third approach which seems to have not been pursued in the literature is a result known as Noether's theorem. There is a Lagrangian formulation for the Euler equation of fluid mechanics. Noether's theorem says that any group action that leaves the Lagrangian action invariant leads to a conserved quantity. This presentation will include a survey of current results regarding acoustic energy and preliminary results on the symmetries of the Lagrangian.

Farassat, F.↗
NASA NTRS2004

Investigation of Polar Stratospheric Cloud Solid Particle Formation Mechanisms Using ILAS and AVHRR Observations in the Arctic

Satellite observations of denitrification and ice clouds in the Arctic lower stratosphere in February 1997 are used with Lagrangian microphysical box model calculations to evaluate nucleation mechanisms of solid polar stratospheric cloud (PSC) particles. The occurrences of ice clouds are not correlated in time and space with the locations of back trajectories of denitrified air masses, indicating that ice particle surfaces are not always a prerequisite for the formation of solid PSCs that lead to denitrification. In contrast, the model calculations incorporating a pseudoheterogeneous freezing process occurring at the vapor-liquid interface can quantitatively explain most of the observed denitrification when the nucleation activation free energy for nitric acid dihydrate formation is raised by only approx.10% relative to the current published values. Once nucleated, the conversion of nitric acid dihydrate to the stable trihydrate phase brings the computed levels of denitrification closer to the measurements. INDEX TERMS: 0305 Atmospheric Composition and Structure: Aerosols and particles (0345, 4801); 0320 Atmospheric Composition and Sb~lctureC: loud physics and chemistry; 0340 Atmospheric Composition and Structure: Middle atmosphere-composition and chemistry

Irie, H.↗
NASA NTRS1999

Drop Breakup in Fixed Bed Flows as Model Stochastic Flow Fields

We examine drop breakup in a class of stochastic flow fields as a model for the flow through fixed fiber beds and to elucidate the general mechanisms whereby drops breakup in disordered, Lagrangian unsteady flows. Our study consists of two parallel streams of investigation. First, large scale numerical simulations of drop breakup in a class of anisotropic Gaussian fields will be presented. These fields are generated spectrally and have been shown in a previous publication to be exact representations of the flow in a dilute disordered bed of fibers if close interactions between the fibers and the drops are dynamically unimportant. In these simulations the drop shape is represented by second and third order small deformation theories which have been shown to be excellent for the prediction of drop breakup in steady strong flows. We show via these simulations that the mechanisms of drop breakup in these flows are quite different than in steady flows. The predominant mechanism of breakup appears to be very short lived twist breakups. Moreover, the occurrence of breakup events is poorly predicted by either the strength of the local flow in which the drop finds itself at breakup, or the degree of deformation that the drop achieves prior to breakup. It is suggested that a correlation function of both is necessary to be predictive of breakup events. In the second part of our research experiments are presented where the drop deformation and breakup in PDMS/polyisobutylene emulsions is considered. We consider very dilute emulsions such that coalescence is unimportant. The flows considered are simple shear and the flow through fixed fiber beds. Turbidity, small angle light scattering, dichroism and microscopy are used to interrogate the drop deformation process in both flows. It is demonstrated that breakup at very low capillary numbers occurs in both flows but larger drop deformation occurs in the fixed bed flow. Moreover, it is witnessed that breakup in the bed occurs continuously during flow and apparently with uniform probability through the bed length. The drop deformations witnessed in our experiments are larger than those predicted by the numerical simulations, and future plans to investigate these differences are discussed.

Shaqfeh, Eric S. G.↗
NASA NTRS1976

Application of a novel finite difference method to dynamic crack problems

A versatile finite difference method (HEMP and HEMP 3D computer programs) was developed originally for solving dynamic problems in continuum mechanics. It was extended to analyze the stress field around cracks in a solid with finite geometry subjected to dynamic loads and to simulate numerically the dynamic fracture phenomena with success. This method is an explicit finite difference method applied to the Lagrangian formulation of the equations of continuum mechanics in two and three space dimensions and time. The calculational grid moves with the material and in this way it gives a more detailed description of the physics of the problem than the Eulerian formulation.

Chen, Y. M.↗
NASA NTRS2006

Simulations of Sea-Ice Dynamics Using the Material-Point Method

In recent years, the availability of large volumes of recorded ice motion derived from high-resolution SAR data has provided an amazingly detailed look at the deformation of the ice cover. The deformation is dominated by the appearance of linear kinematic features that have been associated with the presence of leads. These remarkable data put us in a position to begin detailed evaluation of current coupled mechanical and thermodynamic models of sea ice. This presentation will describe the material point method (MPM) for solving these model equations. MPM is a numerical method for continuum mechanics that combines the best aspects of Lagrangian and Eulerian discretizations. The material points provide a Lagrangian description of the ice that models convection naturally. Thus, properties such as ice thickness and compactness are computed in a Lagrangian frame and do not suffer from errors associated with Eulerian advection schemes, such as artificial diffusion, dispersion, or oscillations near discontinuities. This desirable property is illustrated by solving transport of ice in uniform, rotational and convergent velocity fields. Moreover, the ice geometry is represented by unconnected material points rather than a grid. This representation facilitates modeling the large deformations observed in the Arctic, as well as localized deformation along leads, and admits a sharp representation of the ice edge. MPM also easily allows the use of any ice constitutive model. The versatility of MPM is demonstrated by using two constitutive models for simulations of wind-driven ice. The first model is a standard viscous-plastic model with two thickness categories. The MPM solution to the viscous-plastic model agrees with previously published results using finite elements. The second model is a new elastic-decohesive model that explicitly represents leads. The model includes a mechanism to initiate leads, and to predict their orientation and width. The elastic-decohesion model can provide similar overall deformation as the viscous-plastic model; however, explicit regions of opening and shear are predicted. Furthermore, the efficiency of MPM with the elastic-decohesive model is competitive with the current best methods for sea ice dynamics. Simulations will also be presented for an area of the Beaufort Sea, where predictions can be validated against satellite observations of the Arctic.

Sulsky, D.↗
NASA NTRS1994

A survey of the core-congruential formulation for geometrically nonlinear TL finite elements

This article presents a survey of the core-congruential formulation (CCF) for geometrically nonlinear mechanical finite elements based on the total Lagrangian (TL) kinematic description. Although the key ideas behind the CCF can be traced back to Rajasekaran and Murray in 1973, it has not subsequently received serious attention. The CCF is distinguished by a two-phase development of the finite element stiffness equations. The initial phase developed equations for individual particles. These equations are expressed in terms of displacement gradients as degrees of freedom. The second phase involves congruential-type transformations that eventually binds the element particles of an individual element in terms of its node-displacement degrees of freedom. Two versions of the CCF, labeled direct and generalized, are distinguished. The direct CCF (DCCF) is first described in general form and then applied to the derivation of geometrically nonlinear bar, and plane stress elements using the Green-Lagrange strain measure. The more complex generalized CCF (GCCF) is described and applied to the derivation of 2D and 3D Timoshenko beam elements. Several advantages of the CCF, notably the physically clean separation of material and geometric stiffnesses, and its independence with respect to the ultimate choice of shape functions and element degrees of freedom, are noted. Application examples involving very large motions solved with the 3D beam element display the range of applicability of this formulation, which transcends the kinematic limitations commonly attributed to the TL description.

Felippa, Carlos A.↗
NASA NTRS1991

Dynamic analysis and control of lightweight manipulators with flexible parallel link mechanisms

The flexible parallel link mechanism is designed for increased rigidity to sustain the buckling when it carries a heavy payload. Compared to a one link flexible manipulator, a two link flexible manipulator, especially the flexible parallel mechanism, has more complicated characteristics in dynamics and control. The objective of this research is the theoretical analysis and the experimental verification of dynamics and control of a two link flexible manipulator with a flexible parallel link mechanism. Nonlinear equations of motion of the lightweight manipulator are derived by the Lagrangian method in symbolic form to better understand the structure of the dynamic model. A manipulator with a flexible parallel link mechanism is a constrained dynamic system whose equations are sensitive to numerical integration error. This constrained system is solved using singular value decomposition of the constraint Jacobian matrix. The discrepancies between the analytical model and the experiment are explained using a simplified and a detailed finite element model. The step response of the analytical model and the TREETOPS model match each other well. The nonlinear dynamics is studied using a sinusoidal excitation. The actuator dynamic effect on a flexible robot was investigated. The effects are explained by the root loci and the Bode plot theoretically and experimentally. For the base performance for the advanced control scheme, a simple decoupled feedback scheme is applied.

Lee, Jeh Won↗
NASA NTRS1994

On the effects of a weak magnetic field on turbulent transport

We discuss the effects of a weak large-scale magnetic field on turbulent transport. We show by means of a series of two-dimensional numerical experiments that turbulent diffusion can be effectively suppressed by a (large scale) magnetic field whose energy is small compared to equipartition. The suppression mechanism is associated with a subtle modification of the Lagrangian energy spectrum, and it does not require any substantial reduction of the turbulent amplitude. We exploit the relation between diffusion and random walking to emphasize that the effect of a large-scale magnetic field is to induce a long-term memory in the field of turbulence. The implications of the general case of three-dimensional transport are briefly discussed.

Cattaneo, F.↗
NASA NTRS1985

Transport characteristics in the middle atmosphere and two-dimensional modeling

Transport mechanisms of tracers in the atmosphere are briefly discussed from a viewpoint of Lagrangian motions of air parcels. The tracers are retained by air parcels themselves. In this regard, both momentum and energy are quite different from chemical tracers. The present problem is what interpretation is best for understanding transport mechanisms of tracers. A method is reviewed and proposed, although conceptually. The numerical model used was a whole hemispheric global climate model. Annual- and zonal-mean diabatic forcing was assumed to drive the general circulation. Time integrations were carried out for about 100 days. The model quasi-equilibrium states were analyzed.

Kida, H.↗
NASA NTRS2009

Spatial and Temporal Extrapolation of Disdrometer Size Distributions Based on a Lagrangian Trajectory Model of Falling Rain

Methodologies to improve disdrometer processing, loosely based on mathematical techniques common to the field of particle flow and fluid mechanics, are examined and tested. The inclusion of advection and vertical wind field estimates appear to produce significantly improved results in a Lagrangian hydrometeor trajectory model, in spite of very strict assumptions of noninteracting hydrometeors, constant vertical air velocity, and time independent advection during the scan time interval. Wind field data can be extracted from each radar elevation scan by plotting and analyzing reflectivity contours over the disdrometer site and by collecting the radar radial velocity data to obtain estimates of advection. Specific regions of disdrometer spectra (drop size versus time) often exhibit strong gravitational sorting signatures, from which estimates of vertical velocity can be extracted. These independent wind field estimates become inputs and initial conditions to the Lagrangian trajectory simulation of falling hydrometeors.

Lane, John E.↗