Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Moment equations”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 595 records · Page 33

Bombardment as a cause of the lunar asymmetry.

The moon is asymmetric in crustal thickness and also in the distribution of maria and gamma radioactivity. Early bombardment of the moon by planetesimals, in both heliocentric and geocentric orbits, is examined as a possible cause of the asymmetries. The presence of a massive companion (earth) causes a spin-orbit coupled moon to be bombarded nonuniformly. The most pronounced local concentration of impacts would have occurred on the west limb of the moon, when it orbited close to the earth, if low-eccentricity heliocentric planetesimals were still abundant in the solar system at that time. A very intense bombardment of this type could have redistributed crustal material on the moon, thinning the west limb crust appreciably. This would have caused a change in position of the principal axes of inertia, and a reorientation of the spin-orbit coupled moon such that the thinnest portion of its crust turned toward one of the poles. Erupting lavas would have preferentially flooded such a thin-crusted, low-lying area. This would have caused another readjustment of principal moments, and a reorientation of the moon such that the mare areas tipped toward the equator.

Wood, J. A.↗

Computation of supersonic turbulent flow past a spinning cone

Computational results are presented for supersonic laminar and turbulent flow past a pointed cone at angle of attack obtained with a parabolic Navier-Stokes marching code. The code takes into account the asymmetries in the flowfield resulting from spinning motion and computes the asymmetric shock shape, crossflow and streamwise shear, heat transfer, crossflow separation, and vortex structure. The Magnus force and moments are also computed. Comparisons are made with other analyses based on boundary-layer equations. For certain laminar flow conditions, an anomaly is discovered in the displacement thickness contribution to the Magnus force when compared with boundary-layer results. For turbulent flow, at small angles of attack, good agreement is obtained with the experimental data and other theoretical results.

Agarwal, R. K.↗

An investigation of empennage buffeting

Progress in the investigation of empennage buffeting in reviewed. In summary, the following tasks were accomplished: relevant literatures was reviewed; equations for calculating structural response were formulated; root-mean-square values of root bending moment for a 65-degree rigid delta wing were calculated and compared with data; and a water-tunnel test program for an F-18 model was completed.

Lan, C. E.↗

Integrated Power and Attitude Control for a Spacecraft with Flywheels and Control Moment Gyroscopes

A law is designed for simultaneous control of the orientation of an Earth-pointing spacecraft, the energy stored by counter-rotating flywheels, and the angular momentum of the flywheels and control moment gyroscopes used together as all integrated set of actuators for attitude control. General. nonlinear equations of motion are presented in vector-dyadic form, and used to obtain approximate expressions which are then linearized in preparation for design of control laws that include feedback of flywheel kinetic energy error as it means of compensating for damping exerted by rotor bearings. Two flywheel 'steering laws' are developed such that torque commanded by all attitude control law is achieved while energy is stored or discharged at the required rate. Using the International Space Station as an example, numerical simulations are performed to demonstrate control about a torque equilibrium attitude and illustrate the benefits of kinetic energy error feedback.

Roithmayr, Carlos M.↗

Dynamics and Control of Attitude, Power, and Momentum for a Spacecraft Using Flywheels and Control Moment Gyroscopes

Several laws are designed for simultaneous control of the orientation of an Earth-pointing spacecraft, the energy stored by counter-rotating flywheels, and the angular momentum of the flywheels and control moment gyroscopes used together as an integrated set of actuators for attitude control. General, nonlinear equations of motion are presented in vector-dyadic form, and used to obtain approximate expressions which are then linearized in preparation for design of control laws that include feedback of flywheel kinetic energy error as a means of compensating for damping exerted by rotor bearings. Two flywheel steering laws are developed such that torque commanded by an attitude control law is achieved while energy is stored or discharged at the required rate. Using the International Space Station as an example, numerical simulations are performed to demonstrate control about a torque equilibrium attitude, and illustrate the benefits of kinetic energy error feedback. Control laws for attitude hold are also developed, and used to show the amount of propellant that can be saved when flywheels assist the CMGs. Nonlinear control laws for large-angle slew maneuvers perform well, but excessive momentum is required to reorient a vehicle like the International Space Station.

Roithmayr, Carlos M.↗

Electromagnetic Monitoring and Control of a Plurality of Nanosatellites

A method for monitoring position of and controlling a second nanosatellite (NS) relative to a position of a first NS. Each of the first and second NSs has a rectangular or cubical configuration of independently activatable, current-carrying solenoids, each solenoid having an independent magnetic dipole moment vector, .mu.1 and .mu.2. A vector force F and a vector torque are expressed as linear or bilinear combinations of the first set and second set of magnetic moments, and a distance vector extending between the first and second NSs is estimated. Control equations are applied to estimate vectors, .mu.1 and .mu.2, required to move the NSs toward a desired NS configuration. This extends to control of N nanosatellites.

Soloway, Donald I.↗

Accretion by rotating magnetic neutron stars. III - Accretion torques and period changes in pulsating X-ray sources

The solutions of the two-dimensional hydromagnetic equations are used to calculate the torque on a magnetic neutron star accreting from a Keplerian disk. It is found that the magnetic coupling between the star and the plasma in the outer transition zone is appreciable; that as a result, the spin-up torque on fast rotators is substantially less than that on slow rotators, and that for sufficiently high stellar angular velocities or sufficiently low mass accretion rates, the rotation of the star can be braked while accretion continues. These results are applied to pulsating X-ray sources, revealing that at high luminosities a star of given spin period rotating in the same direction as the disk can experience either spin-up or spin-down, depending on its luminosity. Also considered are the general problem of interpreting period changes in pulsating X-ray sources, and the dipole magnetic moments of nine pulsating X-ray sources are estimated by fitting the theoretical spin-up equation to estimates of the average luminosity and spin-up rate of each source.

Ghosh, P.↗

Identification of hot water end-use process of electric water heaters from energy measurements

This paper presents an algorithm for the identification of parameters for a stochastic hot water end-use process that drives a homogeneous population of thermostatically controlled electric water heaters (EWH). Usually, only metered interval consumption data (kWh) is collected and the hot water end-use process is unobservable to utility and aggregators. However, the availability of EWHs for demand response (DR) is closely coupled with the hot water end-use process. In this context, the hot water end-use process is modeled as a two-state Markov chain (Use / No use), which causes the thermostatic ON-OFF switching process to behave as a Markov renewal process (MRP). A set of first passage-time problems is developed to obtain the moments of the transition probability densities of the MRP. These problems are addressed by establishing a system of coupled partial differential equations characterizing the temperature evolution of the EWH population. A key quantity in the methodology for estimating the parameters is the total time an EWH is ON within a period of interest. It is referred to as the total busy time. Total busy time in this approach is a random variable for which analytical expressions of the moments are developed as a function of the metered window length. The latter expressions become the basis of a hot water demand model identification algorithm which is validated using agent-based simulations of EWHs.

42 ENGINEERING↗

On the equation of state of solar wind ions derived from Helios measurements

The radial evolution of such adiabatic invariants as the ion magnetic moments are studied on the basis of solar wind ion velocity distribution observations made by the Helios spacecraft between 0.3 and 1 AU. Significant differences between proton and alpha-particle parameters in wind velocity dependence are noted, and adiabaticity is on the average found to be violated. This violation is interpreted as evidence that protons are heated perpendicular to the field in fast streams. The contribution of the differential streaming energy to the total internal energy of the ions is also considered, and average heliocentric radial profiles for the ion heat fluxes are presented together with an examination of a possible ion heat flux role in the supply of thermal energy during the winds radial expansion. The present findings suggest that wave-particle interactions, and/or Coulomb collisions, are required to explain solar wind ion thermal energy states and radial temperature profiles.

Marsch, E.↗

Modeling of surface mechanical behaviors of soft elastic solids: theory and examples

Surfaces of soft solids can have significant surface stress, extensional modulus and bending stiffness. Previous theoretical studies have usually examined cases in which both the surface stress and bending stiffness are constant, assuming small deformation. In this work we consider a general formulation in which the surface can support large deformation and carry both surface stresses and surface bending moments. We show that the large deformation theory can be reduced to the classical linear theory (Shuttleworth equation). We obtain exact solutions for problems of an inflated cylindrical shell and bending of a plate with a finite thickness. Our analysis illustrates the different manners in which surface stiffening and surface bending stabilize these structures. We discuss how the complex surface constitutive behaviors affect the stress field of the bulk. Our calculation provides insights into effects of strain-dependent surface stress and surface bending in the large deformation regime, and can be used as a model to implement surface finite elements to study large deformation of complex structures.

36 MATERIALS SCIENCE↗

Flexible robot control: Modeling and experiments

Described here is a model and its use in experimental studies of flexible manipulators. The analytical model uses the equivalent of Rayleigh's method to approximate the displaced shape of a flexible link as the static elastic displacement which would occur under end rotations as applied at the joints. The generalized coordinates are thereby expressly compatible with joint motions and rotations in serial link manipulators, because the amplitude variables are simply the end rotations between the flexible link and the chord connecting the end points. The equations for the system dynamics are quite simple and can readily be formulated for the multi-link, three-dimensional case. When the flexible links possess mass and (polar moment of) inertia which are small compared to the concentrated mass and inertia at the joints, the analytical model is exact and displays the additional advantage of reduction in system dimension for the governing equations. Four series of pilot tests have been completed. Studies on a planar single-link system were conducted at Carnegie-Mellon University, and tests conducted at Toshiba Corporation on a planar two-link system were then incorporated into the study. A single link system under three-dimensional motion, displaying biaxial flexure, was then tested at Carnegie-Mellon.

Oppenheim, Irving J.↗

Quadrupole topological photonic crystals

Quadrupole topological phases, exhibiting protected boundary states that are themselves topological insulators of lower dimensions, have recently been of great interest. Extensions of these ideas from current tight binding models to continuum theories for realistic materials require the identification of quantized invariants describing the bulk quadrupole order. Here we identify the analog of quadrupole order in Maxwell’s equations for a gyromagnetic photonic crystal (PhC) through a double-band-inversion process. The quadrupole moment is quantized by the simultaneous presence of crystalline symmetry and broken time-reversal symmetry, which is confirmed using three independent methods: analysis of symmetry eigenvalues, numerical calculations of the nested Wannier bands and the expectation value of the quadrupole operator. Furthermore, we reveal the boundary manifestations of quadrupole phases as quantized edge polarizations and fractional corner charges. The latter are the consequence of a filling anomaly of energy bands as first predicted in electronic systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Statistics of Green's functions on a disordered Cayley tree and the validity of forward scattering approximation

The accuracy of the forward scattering approximation for two-point Green's functions of the Anderson localization model on the Cayley tree is studied. A relationship between the moments of the Green's function and the largest eigenvalue of the linearized transfer-matrix equation is proved in the framework of the supersymmetric functional-integral method. The new large-disorder approximation for this eigenvalue is derived and its accuracy is established. Using this approximation the probability distribution of the two-point Green's function is found and compared with that in the forward scattering approximation (FSA). It is shown that FSA overestimates the role of resonances and thus the probability for the Green's function to be significantly larger than its typical value. The error of FSA increases with increasing the distance between points in a two-point Green's function.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Termination of the solar wind in the hot, partially ionized interstellar medium

Theoretical foundations for understanding the problem of the termination of the solar wind are reexamined in the light of most recent findings concerning the states of the solar wind and the local interstellar medium. The investigation suggests that a simple extention of Parker's (1961) analytical model provides a useful approximate description of the combined solar wind, interstellar wind plasma flowfield under conditions presently thought to occur. A linear perturbation solution exhibiting both the effects of photoionization and charge exchange is obtained for the supersonic solar wind. A numerical algorithm is described for computing moments of the non-equilibrium hydrogen distribution function and associated source terms for the MHD equations. Computed using the algorithm in conjunction with the extended Parker solution to approximate the plasma flowfield, profiles of hydrogen number density are given in the solar wind along the upstream and downstream axes of flow with respect to the direction of the interstellar wind. Predictions of solar Lyman-alpha backscatter intensities to be observed at 1 a.u. have been computed, in turn, from a set of such hydrogen number density profiles varied over assumed conditions of the interstellar wind.

Lombard, C. K.↗

Shear flow aerodynamics - Lifting surface theory

A lifting surface theory based on a parallel shear flow model is presented for steady, incompressible flows. The theory is intended to account approximately for the presence of a boundary layer. The method of Fourier transforms is used to calculate the pressure on a surface of infinite extent and arbitrary contour. Immediately above the surface is a region of sheared flow (the boundary layer), outside of which the flow velocity is constant. The Fourier transform of the pressure on this surface is used to derive the shear flow equivalent to the kernel function of classical potential flow lifting surface theory. The kernel function provides an integral relation between the upwash at a given point on the surface and the pressure everywhere on the surface. This relation is treated as an integral equation for the pressure, and is solved numerically. Computations are presented for the lift and pitching moment on a flat plate in two-dimensional flow, and for flat, rectangular wings of aspect ratio 1, 2, and 5. As expected, the shear layer decreases the lift curve slope; however, the shear layer (whose thickness is constant along the wing chord) has little effect on the center of pressure.

Ventres, C. S.↗

Theory of idealized two-dimensional ballute in Newtonian hypersonic flow

A differential equation governing the geometry of a two-dimensional ballute in hypersonic flow and its constraining boundary conditions are derived under idealized assumptions. By solving these equations, the shape of the ballute is determined over a range of conditions. Lift, drag, pitching moment, and the allowed limit of center-of-gravity location for stability (meta-center) are then calculated using Newtonian hypersonic approximation. It is shown that the meta-center occurs near the forward end because of compliance of the ballute membrane to the shock layer pressures, especially at low free-stream densities. In order for the vehicle employing the ballute to be stable at all densities, the center of gravity must be within approximately the forward 20 percent of overall length of the vehicle. However, typical flight trajectories of an aeroassisted orbital transfer vehicle employing the ballute for aerobraking show that the vehicle may be able to complete its atmospheric flight without tumbling provided that the center of gravity is located within the forward 43 percent of the vehicle length because of the relatively short duration of flight through the destabilizing low-density regime.

Park, C.↗

A second-order shock-expansion method applicable to bodies of revolution near zero lift

A second-order shock-expansion method applicable to bodies of revolution is developed by the use of the predictions of the generalized shock-expansion method in combination with characteristics theory. Equations defining the zero-lift pressure distributions and the normal-force and pitching-moment derivatives are derived. Comparisons with experimental results show that the method is applicable at values of the similarity parameter, the ratio of free-stream Mach number to nose fineness ratio, from about 0.4 to 2.

Source record↗