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NASA NTRS1972

Integrated dynamic analysis simulation of space stations with controllable solar array

A methodology is formulated and presented for the integrated structural dynamic analysis of space stations with controllable solar arrays and non-controllable appendages. The structural system flexibility characteristics are considered in the dynamic analysis by a synthesis technique whereby free-free space station modal coordinates and cantilever appendage coordinates are inertially coupled. A digital simulation of this analysis method is described and verified by comparison of interaction load solutions with other methods of solution. Motion equations are simulated for both the zero gravity and artificial gravity (spinning) orbital conditions. Closed loop controlling dynamics for both orientation control of the arrays and attitude control of the space station are provided in the simulation by various generic types of controlling systems. The capability of the simulation as a design tool is demonstrated by utilizing typical space station and solar array structural representations and a specific structural perturbing force. Response and interaction load solutions are presented for this structural configuration and indicate the importance of using an integrated type analysis for the predictions of structural interactions.

Heinrichs, J. A.↗

NASA NTRS1973

The orbital mechanics of flight mechanics

A reference handbook on modern dynamic orbit theory is presented. Starting from the most basic inverse-square law, the law of gravity for a sphere is developed, and the motion of point masses under the influence of a sphere is considered. The reentry theory and the orbital theory are discussed along with the relative motion between two bodies in orbit about the same planet. Relative-motion equations, rectangular coordinates, and the mechanics of simple rigid bodies under the influence of a gravity gradient field are also discussed.

Dunning, R. S.↗

NASA NTRS1979

Equation modifying program, L219 (EQMOD). Volume 2: Supplemental system design and maintenance document

A digital computer program, L219 (EQMOD), available for execution on the CDC 6600 is described. The program modifies matrices according to card input instructions and prepares magnetic files of matrices suitable for use in the linear systems analysis program (QR) and the random harmonic analysis program L221 (TEV156). The particular field of application of the program is the modification of the theoretical equations of motion and load equations generated in DYLOFLEX by the equation of motion program (L217) and the load equation program (L218), respectively.

Hirayama, M. Y.↗

NASA NTRS1983

Special cases of friction and applications

Two techniques for reducing friction forces are presented. The techniques are applied to the generalized problem of reducing the friction between kinematic pairs which connect a moveable link to a frame. The basic principles are: (1) Let the moveable link be supported by two bearings where the relative velocities of the link with respect to each bearing are of opposite directions. Thus the resultant force (torque) of friction acting on the link due to the bearings is approximately zero. Then, additional perturbation of motion parallel to the main motion of the moveable link will require only a very small force; (2) Let the perturbation in motion be perpendicular to the main motion. Equations are developed which explain these two methods. The results are discussed in relation to friction in geared couplings, gyroscope gimbal bearings and a rotary conveyor system. Design examples are presented.

Litvin, F. L.↗

NASA NTRS1984

Implementation of the Sun Position Calculation in the PDC-1 Control Microprocessor

The several computational approaches to providing the local azimuth and elevation angles of the Sun as a function of local time and then the utilization of the most appropriate method in the PDC-1 microprocessor are presented. The full algorithm, the FORTRAN form, is felt to be very useful in any kind or size of computer. It was used in the PDC-1 unit to generate efficient code for the microprocessor with its floating point arithmetic chip. The balance of the presentation consists of a brief discussion of the tracking requirements for PPDC-1, the planetary motion equations from the first to the final version, and the local azimuth-elevation geometry.

Stallkamp, J. A.↗

NASA NTRS1984

Special cases of friction and applications

Litvin, F. L.↗

NASA NTRS1985

Eigenvalues and stability problems of rotors

The essential theoretical results of the application of a developed transfer matrix method to the free transverse vibration of a rotor are shown. Gyroscopic and shear effects, rotary inertia, and external and internal damping as well as the influence of sleeve bearings and rotor supports are taken into consideration. The eigenvalues of the motion equations of the rotor are searched by using a modified determinant method.

Walczyk, Z.↗

NASA NTRS1987

The dynamics and control of the Space Station polar platform

The Space Station polar platform will carry a variety of earth observation instruments for NASA and the National Oceanic and Atmospheric Administration. In this paper, the asymmetrical platform is modeled as three connected rigid bodies. A generalized angular momentum equation is employed to derive the rotational equations of motion. These equations are linearized and used for preliminary sizing of control devices using a classical control approach. Two control systems are considered to stabilize the platform and satisfy the pointing requirements. The first system is composed of a single variable-speed, double-gimbaled momentum wheel and the second consists of three-reaction wheels. The performance of each system is assessed using a linear optimal control approach.

Wahbah, M. M.↗

NASA NTRS1989

Dust formation around M-type stars

IRAS LRS spectra of M Mira variable have shown variation in the appearance of the 9.7 micron silicate feature, which is correlated with the shape of light curve. The LRS spectra of 100 Mira variables have been studied using simple dust shell models containing mixtures of silicate and aluminum oxide dust grains. It has been shown that the aluminum oxide grains account for the observed broad feature around 12 microns and that the variation of the spectra can be interpreted in terms of the variation of the temperature at the inner boundary of silicate dust shell. It has been proposed that silicate mantle growth on aluminum oxide grains is a possible explanation for the results. In this report, the model spectra are calculated taking account of silicate mantle growth, and the physical parameters which may determine the appearance of the 9.7 micron feature in M Mira variables are investigated. In the model calculation it is assumed that aluminum oxide grains are already formed at the bottom of the circumstellar envelope because of their high condensation temperature. The growth of silicate mantle and the motion of gas and grains from r=r(sub 0), where the mantle growth starts, are investigated. Sticking and sputtering processes due to the relative motion of grain to the ambient gas are taken into account. The thermal velocity is assumed to be negligible to the drift velocity. Acceleration by radiation pressure is considered in the gas motion equation. The formal solution is integrated to obtain the emergent spectra. Physical conditions inside r(sub 0) are regarded as boundary conditions. Observed spectra are compared to model spectra to investigate the conditions at the bottom of circumstellar envelope. In modeling the envelope, a parameter C(sub l) is introduced to take account of the density fluctuation of the envelope phenomenologically.

Onaka, Takashi↗

NASA NTRS1993

Algorithm and code development for unsteady three-dimensional Navier-Stokes equations

In the last two decades, there have been extensive developments in computational aerodynamics, which constitutes a major part of the general area of computational fluid dynamics. Such developments are essential to advance the understanding of the physics of complex flows, to complement expensive wind-tunnel tests, and to reduce the overall design cost of an aircraft, particularly in the area of aeroelasticity. Aeroelasticity plays an important role in the design and development of aircraft, particularly modern aircraft, which tend to be more flexible. Several phenomena that can be dangerous and limit the performance of an aircraft occur because of the interaction of the flow with flexible components. For example, an aircraft with highly swept wings may experience vortex-induced aeroelastic oscillations. Also, undesirable aeroelastic phenomena due to the presence and movement of shock waves occur in the transonic range. Aeroelastically critical phenomena, such as a low transonic flutter speed, have been known to occur through limited wind-tunnel tests and flight tests. Aeroelastic tests require extensive cost and risk. An aeroelastic wind-tunnel experiment is an order of magnitude more expensive than a parallel experiment involving only aerodynamics. By complementing the wind-tunnel experiments with numerical simulations the overall cost of the development of aircraft can be considerably reduced. In order to accurately compute aeroelastic phenomenon it is necessary to solve the unsteady Euler/Navier-Stokes equations simultaneously with the structural equations of motion. These equations accurately describe the flow phenomena for aeroelastic applications. At Ames a code, ENSAERO, is being developed for computing the unsteady aerodynamics and aeroelasticity of aircraft and it solves the Euler/Navier-Stokes equations. The purpose of this contract is to continue the algorithm enhancements of ENSAERO and to apply the code to complicated geometries. During the last year, the geometric capability of the code was extended to simulate transonic flows, a wing with oscillating control surface. Single-grid and zonal approaches were tested. For the zonal approach, a new interpolation technique was introduced. The key development of the algorithm was an interface treatment between moving zones for a control surface using the virtual-zone concept. The work performed during the period, 1 Apr. 1992 through 31 Mar. 1993 is summarized. Additional details on the various aspects of the study are given in the Appendices.

Obayashi, Shigeru↗

NASA NTRS1952

Calculation of the lateral-dynamic stability of aircraft

Graphs and formulas are given with the aid of which all the aerodynamic coefficients required for computing the lateral dynamic stability can be determined. A number of numerical examples are given for obtaining the stability derivatives and solving the characteristic-stability equation. Approximate formulas are derived with the aid of which rapid preliminary computations may be made and the stability coefficients corrected for certain modifications of the airplane. A derivation of the lateral-dynamic-stability equations is included.

STABILITY, LATERAL - DYNAMIC↗

NASA NTRS1940

Variation in Velocity Profile with Change in Surface Roughness of Boundary

The present report deals with the variation of a turbulent velocity profile in flow from rough to smooth wall and vice versa. Expressions obtained for the shear-stress distribution with respect to the distance from the point of junction of the different roughnesses and from the wall distance, are utilized to ascertain the developing velocity distributions. Under simplified assumptions, the use of these formulas renders possible the integration of the motion equations for the shear stress. This calculation is carried out and compared with the experiments.

Jacobs, W↗

NASA NTRS1994

Algorithm and code development for unsteady three-dimensional Navier-Stokes equations

Aeroelastic tests require extensive cost and risk. An aeroelastic wind-tunnel experiment is an order of magnitude more expensive than a parallel experiment involving only aerodynamics. By complementing the wind-tunnel experiments with numerical simulations, the overall cost of the development of aircraft can be considerably reduced. In order to accurately compute aeroelastic phenomenon it is necessary to solve the unsteady Euler/Navier-Stokes equations simultaneously with the structural equations of motion. These equations accurately describe the flow phenomena for aeroelastic applications. At ARC a code, ENSAERO, is being developed for computing the unsteady aerodynamics and aeroelasticity of aircraft, and it solves the Euler/Navier-Stokes equations. The purpose of this cooperative agreement was to enhance ENSAERO in both algorithm and geometric capabilities. During the last five years, the algorithms of the code have been enhanced extensively by using high-resolution upwind algorithms and efficient implicit solvers. The zonal capability of the code has been extended from a one-to-one grid interface to a mismatching unsteady zonal interface. The geometric capability of the code has been extended from a single oscillating wing case to a full-span wing-body configuration with oscillating control surfaces. Each time a new capability was added, a proper validation case was simulated, and the capability of the code was demonstrated.

Obayashi, Shigeru↗

NASA NTRS1996

Controlled Quantum Packets

We look at time evolution of a physical system from the point of view of dynamical control theory. Normally we solve motion equation with a given external potential and we obtain time evolution. Standard examples are the trajectories in classical mechanics or the wave functions in Quantum Mechanics. In the control theory, we have the configurational variables of a physical system, we choose a velocity field and with a suited strategy we force the physical system to have a well defined evolution. The evolution of the system is the 'premium' that the controller receives if he has adopted the right strategy. The strategy is given by well suited laboratory devices. The control mechanisms are in many cases non linear; it is necessary, namely, a feedback mechanism to retain in time the selected evolution. Our aim is to introduce a scheme to obtain Quantum wave packets by control theory. The program is to choose the characteristics of a packet, that is, the equation of evolution for its centre and a controlled dispersion, and to give a building scheme from some initial state (for example a solution of stationary Schroedinger equation). It seems natural in this view to use stochastic approach to Quantum Mechanics, that is, Stochastic Mechanics [S.M.]. It is a quantization scheme different from ordinary ones only formally. This approach introduces in quantum theory the whole mathematical apparatus of stochastic control theory. Stochastic Mechanics, in our view, is more intuitive when we want to study all the classical-like problems. We apply our scheme to build two classes of quantum packets both derived generalizing some properties of coherent states.

DeMartino, Salvatore↗

NASA NTRS1965

Introduction to SST-ATC Study Program

The purpose of this brief introduction is to define the objectives of the program and to describe the manner in which it is being pursued. The study is directed toward problems anticipated with the introduction of the supersonic transport into the air-traffic-control system. The primary objectives are: (1) The determination of the effects of the SST (supersonic transport) on requirements of the ATC (air traffic control) system. (2) The determination of the effects of the ATC system on requirements for the SST design and for its equipment. Basically, the program is a simulation effort involving equipment both at Langley and at the NAFEC facility. A block diagram illustrating the manner in which the equipment of the two agencies has been integrated to carry out the program. The Langley equipment includes a cockpit, or flight compartment that is generally representative of transport equipment, and an analog computer for solving the six-degree-of-freedom motion equations for an aircraft having the characteristics of the SST design under study.

Toll, Thomas A.↗

NASA NTRS2000

SHIVA: Spaceflight Holography Investigation in a Virtual Apparatus

SHIVA, a NASA spaceflight program, will exploit a unique, holography-based, diagnostics tool to test and apply a new, more general analytical solution to a fundamental equation of motion. The equation describes particle dynamics in fluids in a microgravity environment, and our solution represents the first analytical solution of it. When gravity is removed the equation becomes much more complex and had been solved previously only by numerical means. After our analytical solution has been validated it will be used as a tool for making additional measurements of the gravity environment. Our experiment will be optimized for testing the model, measuring g, g-jitter, and other microgravity phenomena. We will also collect data for which no current theory exists, This paper describes ground experiments and analysis that have been conducted by the investigator team to support the flight experiment.

Trolinger, James D.↗

NASA NTRS2009

Complexity for Survival of Living Systems

A logical connection between the survivability of living systems and the complexity of their behavior (equivalently, mental complexity) has been established. This connection is an important intermediate result of continuing research on mathematical models that could constitute a unified representation of the evolution of both living and non-living systems. Earlier results of this research were reported in several prior NASA Tech Briefs articles, the two most relevant being Characteristics of Dynamics of Intelligent Systems (NPO- 21037), NASA Tech Briefs, Vol. 26, No. 12 (December 2002), page 48; and Self-Supervised Dynamical Systems (NPO- 30634) NASA Tech Briefs, Vol. 27, No. 3 (March 2003), page 72. As used here, living systems is synonymous with active systems and intelligent systems. The quoted terms can signify artificial agents (e.g., suitably programmed computers) or natural biological systems ranging from single-cell organisms at one extreme to the whole of human society at the other extreme. One of the requirements that must be satisfied in mathematical modeling of living systems is reconciliation of evolution of life with the second law of thermodynamics. In the approach followed in this research, this reconciliation is effected by means of a model, inspired partly by quantum mechanics, in which the quantum potential is replaced with an information potential. The model captures the most fundamental property of life - the ability to evolve from disorder to order without any external interference. The model incorporates the equations of classical dynamics, including Newton s equations of motion and equations for random components caused by uncertainties in initial conditions and by Langevin forces. The equations of classical dynamics are coupled with corresponding Liouville or Fokker-Planck equations that describe the evolutions of probability densities that represent the uncertainties. The coupling is effected by fictitious information-based forces that are gradients of the information potential, which, in turn, is a function of the probability densities. The probability densities are associated with mental images both self-image and nonself images (images of external objects that can include other agents). The evolution of the probability densities represents mental dynamics. Then the interaction between the physical and metal aspects of behavior is implemented by feedback from mental to motor dynamics, as represented by the aforementioned fictitious forces. The interaction of a system with its self and nonself images affords unlimited capacity for increase of complexity. There is a biological basis for this model of mental dynamics in the discovery of mirror neurons that learn by imitation. The levels of complexity attained by use of this model match those observed in living systems. To establish a mechanism for increasing the complexity of dynamics of an active system, the model enables exploitation of a chain of reflections exemplified by questions of the form, "What do you think that I think that you think...?" Mathematically, each level of reflection is represented in the form of an attractor performing the corresponding level of abstraction with more details removed from higher levels. The model can be used to describe the behaviors, not only of biological systems, but also of ecological, social, and economics ones.

Zak, Michail↗

NASA NTRS2011

Analysis of Separation Corridors for Visiting Vehicles from the International Space Station

The International Space Station (ISS) is a very dynamic vehicle with many operational constraints that affect its performance, operations, and vehicle lifetime. Most constraints are designed to alleviate various safety concerns that are a result of dynamic activities between the ISS and various Visiting Vehicles (VVs). One such constraint that has been in place for Russian Vehicle (RV) operations is the limitation placed on Solar Array (SA) positioning in order to prevent collisions during separation and subsequent relative motion of VVs. An unintended consequence of the SA constraint has been the impacts to the operational flexibility of the ISS resulting from the reduced power generation capability as well as from a reduction in the operational lifetime of various SA components. The purpose of this paper is to discuss the technique and the analysis that were applied in order to relax the SA constraints for RV undockings, thereby improving both the ISS operational flexibility and extending its lifetime for many years to come. This analysis focused on the effects of the dynamic motion that occur both prior to and following RV separations. The analysis involved a parametric approach in the conservative application of various initial conditions and assumptions. These included the use of the worst case minimum and maximum vehicle configurations, worst case initial attitudes and attitude rates, and the worst case docking port separation dynamics. Separations were calculated for multiple ISS docking ports, at varied deviations from the nominal undocking attitudes and included the use of two separate attitude control schemes: continuous free-drift and a post separation attitude hold. The analysis required numerical propagation of both the separation motion and the vehicle attitudes using 3-degree-of-freedom (DOF) relative motion equations coupled with rigid body rotational dynamics to generate a large set of separation trajectories.

Zaczek, Mariusz P.↗