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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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17 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

Approximating linearizations for nonlinear systems

The following problem is examined: given a nonlinear control system dot-x(t) = f(x(t)) + the sum to m terms(i=1) u sub i (t)g sub i (x(t)) on R(n) and a point x(0) in R(n), approximate the system near x(0) by a linear system. One approach is to use the usual Taylor series linearization. However, the controllability properties of both the nonlinear and linear systems depend on certain Lie brackets of the vector field under consideration. This suggests that a linear approximation based on Lie bracket matching should be constructed at x(0). In general, the linearizations based on the Taylor method and the Lie bracket approach are different. However, under certain mild assumptions, it is shown that there is a coordinate system for R(n) near x(0) in which these two types of linearizations agree. The importance of this agreement is indicated by examining the time responses of the nonlinear system and its linear approximation and comparing the lower order kernels in Volterra expansions of each.

Hunt, L. R.↗
NASA NTRS1986

Approximating linearizations for nonlinear systems

The following problem is examined: given a nonlinear control system dot-x(t) = f(x/t/) + the sum to m terms (i = 1) u sub i (t)g sub i (x/t/) on R(n) and a point x(0) in R(n), approximate the system near x(0) by a linear system. One approach is to use the usual Taylor series linearization. However, the controllability properties of both the nonlinear and linear systems depend on certain Lie brackets of the vector field under consideration. This suggests that a linear approximation based on Lie bracket matching should be constructed at x(0). In general, the linearizations based on the Taylor method and the Lie bracket approach are different. However, under certain mild assumptions, it is shown that there is a coordinate system for R(n) near x(0) in which these two types of linearizations agree. The importance of this agreement is indicated by examining the time responses of the nonlinear system and its linear approximation and comparing the lower order kernels in Volterra expansions of each.

Hunt, L. R.↗
NASA NTRS1986

A canonical expansion for nonlinear systems

The importance of differential geometry, particularly Lie brackets of vector fields, in the study of nonlinear systems is well established. Under very mild assumptions, it is shown that a real-analytic nonlinear system has an expansion in which the coefficients are computed in terms of Lie brackets. This expansion occurs in a special coordinate system. The concept of a pure feedback system is also explained. For control design involving a nonlinear system, one approach is to put the system in its canonical expansion and approximate by that part having only feedback paths.

Su, R.↗
NASA NTRS1983

Linear approximations of nonlinear systems

The development of a method for designing an automatic flight controller for short and vertical take off aircraft is discussed. This technique involves transformations of nonlinear systems to controllable linear systems and takes into account the nonlinearities of the aircraft. In general, the transformations cannot always be given in closed form. Using partial differential equations, an approximate linear system called the modified tangent model was introduced. A linear transformation of this tangent model to Brunovsky canonical form can be constructed, and from this the linear part (about a state space point x sub 0) of an exact transformation for the nonlinear system can be found. It is shown that a canonical expansion in Lie brackets about the point x sub 0 yields the same modified tangent model.

Hunt, L. R.↗
NASA NTRS1983

Linear approximations of nonlinear systems

A method for designing an automatic flight controller for short and vertical takeoff aircraft is presently being developed at NASA Ames Research Center. This technique involves transformations of nonlinear systems to controllable linear systems and takes into account the nonlinearities of the aircraft. In general, the transformations cannot always be given in closed form. Using partial differential equations, an approximate linear system, called the modified tangent model, was recently introduced. A linear transformation of this tangent model to Brunovsky canonical form can be constructed, and from this an approximation of an exact transformation for the nonlinear system can be found. It is shown that a canonical expansion in Lie brackets about the point x(0) yields the same modified tangent model.

Hunt, L. R.↗
NASA NTRS1989

Labeled trees and the efficient computation of derivations

The effective parallel symbolic computation of operators under composition is discussed. Examples include differential operators under composition and vector fields under the Lie bracket. Data structures consisting of formal linear combinations of rooted labeled trees are discussed. A multiplication on rooted labeled trees is defined, thereby making the set of these data structures into an associative algebra. An algebra homomorphism is defined from the original algebra of operators into this algebra of trees. An algebra homomorphism from the algebra of trees into the algebra of differential operators is then described. The cancellation which occurs when noncommuting operators are expressed in terms of commuting ones occurs naturally when the operators are represented using this data structure. This leads to an algorithm which, for operators which are derivations, speeds up the computation exponentially in the degree of the operator. It is shown that the algebra of trees leads naturally to a parallel version of the algorithm.

Grossman, Robert↗
NASA NTRS1990

Evaluation of expressions involving higher order derivations

The local geometric properties of a nonlinear control system defined by vector fields E(sub 1),..., E(sub M) are determined by the algebraic properties of the iterated Lie brackets of the E(sub j)'s. The problem of rewriting expressions is examined involving the E(sub j)'s in terms of the D(sub mu)'s in such a way as to handle effectively any cancellation occurring due to commuting of the D(sub mu)'s. A data structure is introduced which allows us to organize the computation to take advantage of the symmetries in the expression and reduce the operation count.

Grossman, Robert↗
NASA NTRS1994

Particle localization, spinor two-valuedness, and Fermi quantization of tensor systems

Recent studies of particle localization shows that square-integrable positive energy bispinor fields in a Minkowski space-time cannot be physically distinguished from constrained tensor fields. In this paper we generalize this result by characterizing all classical tensor systems, which admit Fermi quantization, as those having unitary Lie-Poisson brackets. Examples include Euler's tensor equation for a rigid body and Dirac's equation in tensor form.

Reifler, Frank↗
NASA NTRS1990

Robot cable-compliant devices

A cable compliant robotic joint includes two U configuration cross section brackets with their U cross sections lying in different planes, one of their brackets being connected to a robot arm and the other to a tool. Additional angle brackets are displaced from the other brackets at corners of the robotic joint. All the brackets are connected by cable segments which lie in one or more planes which are perpendicular to the direction of tool travel as it approaches a work object. The compliance of the joint is determined by the cable segment characteristics, such as their length, material, angle, stranding, pretwisting, and prestressing.

Kerley, James J., Jr.↗
NASA NTRS1975

The geometric approach to sets of ordinary differential equations and Hamiltonian dynamics

The calculus of differential forms is used to discuss the local integration theory of a general set of autonomous first order ordinary differential equations. Geometrically, such a set is a vector field V in the space of dependent variables. Integration consists of seeking associated geometric structures invariant along V: scalar fields, forms, vectors, and integrals over subspaces. It is shown that to any field V can be associated a Hamiltonian structure of forms if, when dealing with an odd number of dependent variables, an arbitrary equation of constraint is also added. Families of integral invariants are an immediate consequence. Poisson brackets are isomorphic to Lie products of associated CT-generating vector fields. Hamilton's variational principle follows from the fact that the maximal regular integral manifolds of a closed set of forms must include the characteristics of the set.

Estabrook, F. B.↗
NASA NTRS1993

Nonlinear modes of the tensor Dirac equation and CPT violation

Recently, it has been shown that Dirac's bispinor equation can be expressed, in an equivalent tensor form, as a constrained Yang-Mills equation in the limit of an infinitely large coupling constant. It was also shown that the free tensor Dirac equation is a completely integrable Hamiltonian system with Lie algebra type Poisson brackets, from which Fermi quantization can be derived directly without using bispinors. The Yang-Mills equation for a finite coupling constant is investigated. It is shown that the nonlinear Yang-Mills equation has exact plane wave solutions in one-to-one correspondence with the plane wave solutions of Dirac's bispinor equation. The theory of nonlinear dispersive waves is applied to establish the existence of wave packets. The CPT violation of these nonlinear wave packets, which could lead to new observable effects consistent with current experimental bounds, is investigated.

Reifler, Frank J.↗
NASA NTRS2006

Past and Future SOHO-Ulysses Quadratures

With the launch of SOHO, it again became possible to carry out quadrature observations. In comparison with earlier observations, the new capabilities of coronal spectroscopy with UVCS and in situ ionization state and composition with Ulysses/SWICS enabled new types of studies. Results from two studies serve as examples: (i) The acceleration profile of wind from small coronal holes. (ii) A high-coronal reconnecting current sheet as the source of high ionization state Fe in a CME at Ulysses. Generally quadrature observations last only for a few days, when Ulysses is within ca. 5 degrees of the limb. This means luck is required for the phenomenon of interest to lie along the radial direction to Ulysses. However, when Ulysses is at high southern latitude in winter 2007 and high northern latitude in winter 2008, there will be unusually favorable configurations for quadrature observations with SOHO and corresponding bracketing limb observations from STEREO A/B. Specifically, Ulysses will be within 5 degrees of the limb from December 2006 to May 2007 and within 10 degrees of the limb from December 2007 to May 2008. These long-lasting quadratures and bracketing STEREO A/B observations overcome the limitations inherent in the short observation intervals of typical quadratures. Furthermore, ionization and charge state measurements like those on Ulysses will also be made on STEREO and these will be essential for identification of CME ejecta - one of the prime objectives for STEREO.

Suess, Steven↗
NASA NTRS2000

Structure of Protoplanetary Environments

Our research focused on the structure and composition of the disks in the T Tau and Haro 6-10 multiple star systems and on the nature of the 'infrared companions' that these systems contain. This work has resulted in two papers, one on T Tau, presently under review at the Astrophysical Journal, and the other, on Haro 6-10, about to be submitted to Astronomy and Astrophysics. In the paper 'Evidence for Extinction and Accretion Variability in T Tau S' by Tracy L. Beck, L. Prato, and M. Simon, we present angularly resolved spectra of T Tau N (the visible star) and T Tau S (the infrared companion, IRC) in the three micrometer water ice-feature and the K-band. Most of the water ice absorption lies along the line of sight to T Tau S, confirming it is seen through stronger obscuration. A decrease in the ice-band absorption toward T Tau S between 12/98 and 1/00, significant, at the two-sigma level, was associated with an increase in its near IR flux. Bracket gamma emission is detected in T Tau N and S, and H2 (2.12 micrometer) emission only toward T Tau S, consistent with previous studies of IRCs. Our results suggest that the near IR variability of T Tau S is probably caused by both variations in accretion rate and extinction. Our paper on Haro 6-10, 'The Near IR and Ice Band Variability of Haro, 6-10' by Ch. Leinert, T.L. Beck, S. Ligori, M. Simon, J. Woitas, and R.R. Howell, represents a fusion of originally independent efforts at the Max Planck Institut fur Astronomie (Heidelberg) and Stony Brook. Our combined observations demonstrate that both Haro 6-10 S (the visible star) and Haro 6-10 N (the IRC) vary significantly in near IR flux on time scales as short as a month. The substantial decrease of Haro 6-10 S in the last four years carries the photometric signature of increased extinction. However, a comparable K-band flux increase of the IRC is associated with a dimming at H so cannot be explained by lower extinction. Absorption in the 3.1 micrometer ice band was always greater toward the IRC during our observations indicating a large amount of obscuring material. We detect variable extinction in the ice-band toward Haro 6-10 S and the IRC, significant at the 3.5-sigma and 2.0-sigma levels, respectively.

Simon, Michal↗
NASA NTRS1978

User's guide to computer programs JET 5A and CIVM-JET 5B to calculate the large elastic-plastic dynamically-induced deformations of multilayer partial and/or complete structural rings

These structural ring deflections lie essentially in one plane and, hence, are called two-dimensional (2-d). The structural rings may be complete or partial; the former may be regarded as representing a fragment containment ring while the latter may be viewed as a 2-d fragment-deflector structure. These two types of rings may be either free or supported in various ways (pinned-fixed, locally clamped, elastic-foundation supported, mounting-bracket supported, etc.). The initial geometry of each ring may be circular or arbitrarily curved; uniform-thickness or variable-thickness rings may be analyzed. Strain-hardening and strain-rate effects of initially-isotropic material are taken into account. An approximate analysis utilizing kinetic energy and momentum conservation relations is used to predict the after-impact velocities of each fragment and of the impact-affected region of the ring; this procedure is termed the collision-imparted velocity method (CIVM) and is used in the CIVM-JET 5 B program. This imparted-velocity information is used in conjunction with a finite-element structural response computation code to predict the transient, large-deflection, elastic-plastic responses of the ring. Similarly, the equations of motion of each fragment are solved in small steps in time. Provisions are made in the CIVM-JET 5B code to analyze structural ring response to impact attack by from 1 to 3 fragments, each with its own size, mass, translational velocity components, and rotational velocity. The effects of friction between each fragment and the impacted ring are included.

Wu, R. W. H.↗
NASA NTRS1988

Locking hinge

The space station configuration currently studied utilizes structures which require struts to be hinged in the middle in the stowed mode and locked into place in the deployed mode. Since there are hundreds of hinges involved, it is necessary that they have simple, positive locking features with a minimum of joint looseness or slack. This invention comprises two similar housings hinged together with a spring loaded locking member which assists in making as well as breaking the lock. This invention comprises a bracket hinge and bracket members with a spring biased and movable locking member. The locking or latch member has ear parts received in locking openings where wedging surfaces on the ear parts cooperate with complimentary surfaces on the bracket members for bringing the bracket members into a tight end-to-end alignment when the bracket members are in an extended position. When the locking member is moved to an unlocking position, pivoting of the hinge about a pivot pin automatically places the locking member to retain the locking member in an unlocked position. In pivoting the hinge from an extended position to a folded position, longitudinal spring members are placed under tension over annular rollers so that the spring tension in a folded position assists in return of the hinge from a folded to an extended position. Novelty lies in the creation of a locking hinge which allows compact storage and easy assembly of structural members having a minimal number of parts.

Wesselski, Clarence J.↗
NASA NTRS2007

Electromechanically Actuated Valve for Controlling Flow Rate

A proposed valve for controlling the rate of flow of a fluid would include an electric-motor-driven ball-screw mechanism for adjusting the seating element of the valve to any position between fully closed and fully open. The motor would be of a type that can be electronically controlled to rotate to a specified angular position and to rotate at a specified rate, and the ball screw would enable accurate linear positioning of the seating element as a function of angular position of the motor. Hence, the proposed valve would enable fine electronic control of the rate of flow and the rate of change of flow. The uniqueness of this valve lies in a high degree of integration of the actuation mechanism with the flow-control components into a single, relatively compact unit. A notable feature of this integration is that in addition to being a major part of the actuation mechanism, the ball screw would also be a flow-control component: the ball screw would be hollow so as to contain part of the main flow passage, and one end of the ball screw would be the main seating valve element. The relationships among the components of the valve are best understood by reference to the figure, which presents meridional cross sections of the valve in the fully closed and fully open positions. The motor would be supported by a bracket bolted to the valve body. By means of gears or pulleys and a timing belt, motor drive would be transmitted to a sleeve that would rotate on bearings in the valve body. A ball nut inside the sleeve would be made to rotate with the sleeve by use of a key. The ball screw would pass through and engage the ball nut. A key would prevent rotation of the ball screw in the valve body while allowing the ball screw to translate axially when driven by the ball nut. The outer surface of the ball screw would be threaded only in a mid-length region: the end regions of the outer surface of the ball screw would be polished so that they could act as dynamic sealing surfaces. The inlet end (the right end as depicted in the figure) of the ball screw would be the main seating valve element: in the fully closed position, it would be pressed against the valve seat, as depicted in the upper part of the figure. A retainer would hold the valve seat in an inlet fitting. In addition, the retainer would be contoured to obtain a specified flow rate as a function of axial position of the ball screw. In the fully closed position, little force would be needed to press the ball screw against the seat because the push bore area upon which the upstream pressure would act would be small. The motor would position and hold the ball screw against the seat, providing the force necessary for sealing. To open the valve to a particular position, the motor would be commanded to rotate to a particular angular position (equivalently, a particular number of revolutions) at a particular rate of rotation within its torque limitations. Once the valve was open, fluid would flow through the inlet fitting and the chamber in the inlet housing, past the seat and its retainer, along the hollow core of the ball screw, and through the outlet housing and outlet fitting. The net force generated from fluid pressure in the open position would be small because the pressure exposed to the push bore areas at the inlet and outlet are nearly equal and the forces generated would be in opposing directions.

Patterson, Paul↗