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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 NTRS1974

The three dimensional motion and stability of a rotating space station: Cable-counterweight configuration

The three dimensional equations of motion for a cable connected space station--counterweight system are developed using a Lagrangian formulation. The system model employed allows for cable and end body damping and restoring effects. The equations are then linearized about the equilibrium motion and nondimensionalized. To first degree, the out-of-plane equations uncouple from the inplane equations. Therefore, the characteristic polynomials for the in-plane and out-of-plane equations are developed and treated separately. From the general in-plane characteristic equation, necessary conditions for stability are obtained. The Routh-Hurwitz necessary and sufficient conditions for stability are derived for the general out-of-plane characteristic equation. Special cases of the in-plane and out-of-plane equations (such as identical end masses, and when the cable is attached to the centers of mass of the two end bodies) are then examined for stability criteria.

Bainum, P. M.↗
NASA NTRS1973

Advanced control concepts

The problems of excess control devices and insufficient trim control capability on shuttle ascent vehicles were investigated. The trim problem is solved at all time points of interest using Lagrangian multipliers and a Simplex based iterative algorithm developed as a result of the study. This algorithm has the capability to solve any bounded linear problem with physically realizable constraints, and to minimize any piecewise differentiable cost function. Both solution methods also automatically distribute the command torques to the control devices. It is shown that trim requirements are unrealizable if only the orbiter engines and the aerodynamic surfaces are used.

Sharp, J. B.↗
NASA NTRS1973

Variational calculations for resonance oscillations of inhomogeneous plasmas

The electrostatic resonance properties of an inhomogeneous plasma column are reported by application of the Rayleigh-Ritz method. A description of the rf equation of motion and pressure term that expresses the system of equations in Euler-Lagrange form is presented. The Rayleigh-Ritz procedure is applied to the corresponding Lagrangian to obtain approximate resonance frequencies and eigenfunctions. An appropriate set of trial coordinate functions is defined, which leads to frequency and eigenfunction estimates.

Peng, Y. K. M.↗
NASA NTRS1974

Finite element formulations for problems of large elastic-plastic deformation

An Eulerian finite element formulation is presented for problems of large elastic-plastic flow. The method is based on Hill's variational principle for incremental deformations, and is suited to isotropically hardening Prandtl-Reuss materials. The formulation is given in a manner which allows any conventional finite element program, for "small strain" elasticplastic analysis, to be simply and rigorously adapted to problems involving arbitrary amounts of deformation and arbitrary levels of stress in comparison to plastic deformation moduli. The method is applied to a necking bifurcation analysis of a bar in plane-strain tension. A unified general formulation of finite element equations, both Lagrangian and Eulerian, for large deformations, with arbitrary choice of the conjugate stress and strain measures, and a discussion is given of other proposed formulations for elastic-plastic finite element analysis at large strain.

Mcmeeking, R. M.↗
NASA NTRS1974

Analytical Dynamics and Nonrigid Spacecraft Simulation

Application to the simulation of idealized spacecraft are considered both for multiple-rigid-body models and for models consisting of combination of rigid bodies and elastic bodies, with the elastic bodies being defined either as continua, as finite-element systems, or as a collection of given modal data. Several specific examples are developed in detail by alternative methods of analytical mechanics, and results are compared to a Newton-Euler formulation. The following methods are developed from d'Alembert's principle in vector form: (1) Lagrange's form of d'Alembert's principle for independent generalized coordinates; (2) Lagrange's form of d'Alembert's principle for simply constrained systems; (3) Kane's quasi-coordinate formulation of D'Alembert's principle; (4) Lagrange's equations for independent generalized coordinates; (5) Lagrange's equations for simply constrained systems; (6) Lagrangian quasi-coordinate equations (or the Boltzmann-Hamel equations); (7) Hamilton's equations for simply constrained systems; and (8) Hamilton's equations for independent generalized coordinates.

Likins, P. W.↗
NASA NTRS1973

Introduction to gasdynamics of explosions

Questions concerning the genesis and sustenance of an explosion are investigated, giving attention to the mechanics of explosions, the gasdynamics of explosions, aspects of technological significance, and future prospects. The dynamics of exothermic processes is discussed together with the most prominent effects of explosions. Blast waves are considered, taking into account conservation principles, blast wave transformation, conservative equations in nondimensional form, the equation of state, Eulerian space profiles, Eulerian time profiles, Lagrangian time profiles, boundary conditions and integral relations, and self-similar flow fields.

Oppenheim, A. K.↗
NASA NTRS1973

Effect of steady state coning angle and damping on whirl flutter stability

The main object of this investigation is to find the effect of the steady state coning angle and the damping at the flapping hinge of the blades on the whirl flutter stability boundary and thus to determine the role they can play in narrowing down the gap between theory and experiment. The governing equations of motion, with these two parameters included are derived by the classical Lagrangian approach using quasi-steady blade element theory for aerodynamic forces. A linearized analysis of these equations is applied to two of the wind tunnel models of the previous investigations. The results indicate that these parameters have a marked effect on stability boundary and they may even change the mode of flutter from backward whirl to forward whirl.

Kaza, K. R. V.↗
NASA NTRS1973

New two-metric theory of gravity with prior geometry

A Lagrangian-based metric theory of gravity is developed with three adjustable constants and two tensor fields, one of which is a nondynamic 'flat space metric' eta. With a suitable cosmological model and a particular choice of the constants, the 'post-Newtonian limit' of the theory agrees, in the current epoch, with that of general relativity theory (GRT); consequently the theory is consistent with current gravitation experiments. Because of the role of eta, the gravitational 'constant' G is time-dependent and gravitational waves travel null geodesics of eta rather than the physical metric g. Gravitational waves possess six degrees of freedom. The general exact static spherically-symmetric solution is a four-parameter family. Future experimental tests of the theory are discussed.

Lightman, A. P.↗
NASA NTRS1974

Conservation of wave action

It is pointed out that two basic principles appear in the theory of wave propagation, including the existence of a phase variable and a law governing the intensity, in terms of a conservation law. The concepts underlying such a conservation law are explored. The waves treated are conservative in the sense that they obey equations derivable from a variational principle applied to a Lagrangian functional. A discrete oscillating system is considered. The approach employed also permits in a natural way the definition of a local action density and flux in problems in which the waves are modal or general.

Hayes, W. D.↗
NASA NTRS1974

The three dimensional motion and stability of a rotating space station-cable-counterweight configuration

The three dimensional equations of motion for a cable connected space station-counterweight system are developed using a Lagrangian formulation. The system model employed allows for cable and end body damping and restoring effects. The equations are then linearized about the equilibrium motion and nondimensionalized. To first degree, the out-of-plane equations uncouple from the in-plane equations. From the general in-plane characteristic equation, necessary conditions for stability are obtained. The Routh-Hurwitz necessary and sufficient conditions for stability are derived for the general out-of-plane characteristic equation. Special cases of the in-plane and out-of-plane equations are then examined for stability. Time constants for the least damped mode are obtained for a range of system parameters by numerical examination of the roots of the in-plane and out-of-plane characteristic polynomials.

Bainum, P. M.↗
NASA NTRS1975

Teleoperator control for passivation of satellites possessing angular momentum

Certain space shuttle missions may require the retrieval of passive spinning and processing satellites. One proposed means of retrieval utilizes a free-flying teleoperator launched from the shuttle. The feasibility of nulling the combined spin and precession (passivation) of a typical rigid satellite is first established using a Lagrangian formulation. It is shown that a proposed asymmetric teleoperator cannot be used for passivation in its present form because it would quickly tumble over after being spun-up to synchronize with the angular rates of the satellite. In addition, a dynamic analysis is made of the combined teleoperator-satellite system where an initial misalignment of their respective angular momentum vectors is assumed.

Nadkarni, A. A.↗
NASA NTRS1975

Three-dimensional dynamics of scientific balloon systems in response to sudden gust loadings

A mathematical model was developed of the three-dimensional dynamics of a high-altitude scientific research balloon system perturbed from its equilibrium configuration by an arbitrary gust loading. The platform is modelled as a system of four coupled pendula, and the equations of motion were developed in the Lagrangian formalism assuming a small-angle approximation. Three-dimensional pendulation, torsion, and precessional motion due to Coriolis forces are considered. Aerodynamic and viscous damping effects on the pendulatory and torsional motions are included. A general model of the gust field incident upon the balloon system was developed. The digital computer simulation program is described, and a guide to its use is given.

Dorsey, D. R., Jr.↗
NASA NTRS1974

Interpretations of the EOLE experiment. I - Temporal variation of Eulerian quantities

The EOLE data were obtained on the basis of the interrogation of nearly 500 constant density balloons by a satellite in a 50 deg inclined orbit with an orbital time of about 100 min. The isosteric surface in which the balloons operated closely approximates the 200-mb isobaric surface. Ambient temperature and pressure were determined by instruments. Lagrangian velocities were calculated from balloon displacements between successive satellite orbits. The properties of the EOLE data are considered together with averaging schemes and data problems, time sections, and questions of hemispheric energetics.

Webster, P. J.↗
NASA NTRS1975

Counterglow from the earth-moon libration points

Results from the OSO-6 Rutgers Zodiacal Light Analyzer experiment show photometric perturbations above the background in the antisun line of sight. Sixteen successive lunations were examined, and the accumulated perturbations show a maximum value in the direction of the L4 and L5 earth-moon libration points. This is interpreted as a counterglow from a cloud of particles at the libration points. The average brightness of these libration clouds is 20 S10 Vis. The average angular size of the libration clouds is approximately 6 degrees. Their position varies from one lunation to the next, within an ellipsoidal zone centered on the libration-point direction, with its semimajor axis, of approximately 6 degrees, nominally in the ecliptic and its semiminor axis, of approximately 2 degrees perpendicular to the ecliptic. The position of these clouds with respect to the Lagrangian L4 and L5 points is towards the moon in the northern summer and away from the moon in the northern winter.

Roach, J. R.↗
NASA NTRS1975

Behavior of matter at superhigh density

The properties of the pion-pion collision in the GeV region are examined in order to provide insights into the behavior of matter at densities greater than 100 Teragrams per cu cm. The predictions based on the Landau model are used to decide upon the value for the speed of sound in the expression pressure equals c(s) squared times the energy density, where c(s) is the speed of sound expressed in units of c. Several pion-pion Lagrangians are analyzed for their predictions on the value of c(s) squared. The fundamental assumption of the Landau model, namely, the laminar nature of the flow, is investigated. It is found that the hadronic matter can become turbulent in the later stages of evolution when Reynolds number of about 4,000 is reached, which gives rise to the possibility of identifying the observed tendency of the pion gas to cluster with the eddies that characterize any turbulent flow.

Canuto, V.↗
NASA NTRS1975

Finite-element formulations for problems of large elastic-plastic deformation

An Eulerian finite element formulation is presented for problems of large elastic-plastic flow. The method is based on Hill's variational principle for incremental deformations, and is ideally suited to isotropically hardening Prandtl-Reuss materials. Further, the formulation is given in a manner which allows any conventional finite element program, for 'small strain' elastic-plastic analysis, to be simply and rigorously adapted to problems involving arbitrary amounts of deformation and arbitrary levels of stress in comparison to plastic deformation moduli. The method is applied to a necking bifurcation analysis of a bar in plane-strain tension. The paper closes with a unified general formulation of finite element equations, both Lagrangian and Eulerian, for large deformations, with arbitrary choice of the conjugate stress and strain measures. Further, a discussion is given of other proposed formulations for elastic-plastic finite element analysis at large strain, and the inadequacies of some of these are commented upon.

Mcmeeking, R. M.↗
NASA NTRS1975

Variational calculations for resonance oscillations of inhomogeneous plasmas

The electrostatic resonance properties of an inhomogeneous plasma column are treated by the Rayleigh-Ritz method. In contrast to Parker, Nickel & Gould (1964), who carried out an exact computation, the present treatment uses a description of the RF equation of motion and pressure term that allows one to express the system of equations in Euler-Lagrange form. The Rayleigh-Ritz procedure is then applied to the corresponding Lagrangian, to obtain approximate resonance frequences and eigenfunctions. An appropriate set of trial coordinate functions is defined, which leads to frequency and eigenfunction estimates in excellent agreement with the work of Parker et al. (1964).

Peng, Y.-K. M.↗
NASA NTRS1974

Canonical fluid thermodynamics

The space-time integral of the thermodynamic pressure plays in a certain sense the role of the thermodynamic potential for compressible adiabatic flow. The stability criterion can be converted into a variational minimum principle by requiring the molar free-enthalpy and temperature to be generalized velocities. In the fluid context, the definition of proper-time differentiation involves the fluid velocity expressed in terms of three particle identity parameters. The pressure function is then converted into a functional which is the Lagrangian density of the variational principle. Being also a minimum principle, the variational principle provides a means for comparing the relative stability of different flows. For boundary conditions with a high degree of symmetry, as in the case of a uniformly expanding spherical gas box, the most stable flow is a rectilinear flow for which the world-trajectory of each particle is a straight line. Since the behavior of the interior of a freely expanding cosmic cloud may be expected to be similar to that of the fluid in the spherical box of gas, this suggests that the cosmic principle is a consequence of the laws of thermodynamics, rather than just an ad hoc postulate.

Schmid, L. A.↗