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All sourcesNASA NTRSDOE OSTI
NASA NTRS1982

Fuel optimal maneuvers of spacecraft about a circular orbit

Fuel optimal maneuvers of spacecraft relative to a body in circular orbit are investigated using a point mass model in which the magnitude of the thrust vector is bounded. All nonsingular optimal maneuvers consist of intervals of full thrust and coast and are found to contain at most seven such intervals in one period. Only four boundary conditions where singular solutions occur are possible. Computer simulation of optimal flight path shapes and switching functions are found for various boundary conditions. Emphasis is placed on the problem of soft rendezvous with a body in circular orbit.

Carter, T. E.↗
NASA NTRS1984

Fuel-optimal maneuvers of a spacecraft relative to a point in circular orbit

Fuel optimal maneuvers of spacecraft relative to a body in circular orbit are investigated using a point mass model in which the magnitude of the thrust vector is bounded. All nonsingular optimal maneuvers consist of intervals of full thrust and coast and are found to contain at most seven such intervals in one period. Only four boundary conditions where singular solutions occur are possible. Computer simulation of optimal flight path shapes and switching functions are found for various boundary conditions. Emphasis is placed on the problem of soft rendezvous with a body in circular orbit.

Carter, T. E.↗
NASA NTRS2010

Equivalent Dipole Vector Analysis for Detecting Pulmonary Hypertension

Various 12-lead ECG criteria have been established to detect right ventricular hypertrophy as a marker of pulmonary hypertension (PH). While some criteria offer good specificity they lack sensitivity because of a low prevalence of positive findings in the PH population. We hypothesized that three-dimensional equivalent dipole (ED) model could serve as a better detection tool of PH. We enrolled: 1) 17 patients (12 female, 5 male, mean age 57 years, range 19-79 years) with echocardiographically detected PH (systolic pulmonary arterial pressure greater than 35 mmHg) and no significant left ventricular disease; and 2) 19 healthy controls (7 female, 12 male, mean age 44, range 31-53 years) with no known heart disease. In each subject we recorded a 5-minute high-resolution 12-lead conventional ECG and constructed principal signals using singular value decomposition. Assuming a standard thorax dimension of an adult person with homogenous and isotropic distribution of thorax conductance, we determined moving equivalent dipoles (ED), characterized by the 3D location in the thorax, dipolar strength and the spatial orientation, in time intervals of 5 ms. We used the sum of all ED vectors in the second half of the QRS complex to derive the amplitude of the right-sided ED vector (RV), if the orientation of ED was to the right side of the thorax, and in the first half the QRS to derive the amplitude of the left-sided vector (LV), if the orientation was leftward. Finally, the parameter RV/LV ratio was determined over an average of 256 complexes. The groups differed in age and gender to some extent. There was a non-significant trend toward higher RV in patients with PH (438 units 284) than in controls (280 plus or minus 140) (p = 0.066) but the overlap was such that RV alone was not a good predictor of PH. On the other hand, the RV/LV ratio was a better predictor of PH, with 11/17 (64.7%) of PH patients but only in 1/19 (5.3%) control subjects having RV/LV ratio greater than or equal to 0.70 (p less than 0.001). The use of ED for evaluating PH shows good specificity at a reasonable sensitivity. The results are limited due to the small study groups and differences in age and gender, but further investigations are warranted, including of ED's diagnostic accuracy for PH versus that of other proposed ECG and VCG criteria.

Harlander, Matevz↗
NASA NTRS1981

Singular perturbation, state aggregation and nonlinear filtering

Consideration is given to a state process evolving in R(n), whose motion is that of a pure jump process in R(n) in the 0(1) time scale, upon which is superimposed a continuous motion along the orbits of a gradient-like vector field g in R(n) in the 0(1/epsilon) time scale. The infinitesimal generator of the state process is, in other words, of the form L + (1/epsilon)g. It follows from the main results presented that the projected filters converge to the finite state Wonham filter corresponding to the problem of estimating the finite state process in the presence of additive white noise.

Hijab, O.↗
NASA NTRS1990

Prediction of vortex shedding from forebodies with chines

An engineering prediction method to calculate vortex shedding from noncircular forebodies with sharp chine edges in subsonic flow at large incidence angles is presented. The forebody is represented by two- and three-dimensional singularities, and the lee side vortex wake is modeled by discrete vortices in crossflow planes along the body. The computational procedure is described, and comparisons of measured and predicted surface pressure distributions and predicted flow field vectors are presented to illustrate the method.

Mendenhall, Michael R.↗
NASA NTRS1974

An Analytical Investigation of Wing-Jet Interaction

The aerodynamic interaction between the wing and an inviscid jet with Mach number nonuniformity is formulated by using a two-vortex-sheet model for the jet. One of the vortex sheets accounts for the induced jet flow and the other the induced outer flow. No additional source distribution is needed for the jet at an angle of attack. The above problem is solved by satisfying the jet and wing tangency and the jet pressure-continuity conditions and using a quasi vortex lattice method for computing the induced flow field. The latter method is derived through theoretical consideration by properly accounting for singularities present in the equations and possesses the same simplicity and generality as the conventional vortex lattice method but has a better rate of numerical convergence. The resulting system of algebraic equations is solved by Purcell's vector method. The numerical formulation is first applied to the wing-slipstream interaction problem. Results for one centered-jet configuration are compared with those predicted by some existing theories.

Lan, E. C.↗
NASA NTRS1987

Evaluation of constraint stabilization procedures for multibody dynamical systems

Comparative numerical studies of four constraint treatment techniques for the simulation of general multibody dynamic systems are presented, and results are presented for the example of a classical crank mechanism and for a simplified version of the seven-link manipulator deployment problem. The staggered stabilization technique (Park, 1986) is found to yield improved accuracy and robustness over Baumgarte's (1972) technique, the singular decomposition technique (Walton and Steeves, 1969), and the penalty technique (Lotstedt, 1979). Furthermore, the staggered stabilization technique offers software modularity, and the only data each solution module needs to exchange with the other is a set of vectors plus a common module to generate the gradient matrix of the constraints, B.

Park, K. C.↗
NASA NTRS1988

Graphical representation of three-dimensional vortical flows by means of helicity density and normalized helicity

The helicity density and normalized helicity are introduced as important tools for the graphical representation of three-dimensional flowfields that contain concentrated vortices. The use of these two quantities filters out the graphical representation of the flowfield regions of low vorticity, as well as regions of high vorticity but low speed where the angle between the velocity and vorticity vectors is large (such as in the boundary layer). Their use permits the researcher to identify and accentuate the concentrated vortices, differentiate between primary and secondary vortices and mark their separation and reattachment lines. The method allows locating the singular points in type I primary separations and tracing the vortex-core streamlines that emanate from them. It also allows locating the vortex-core axes in flows of other types.

Seginer, Arnan↗
NASA NTRS1979

Topology of two-dimensional and three-dimensional separated flows

It is shown that topology rules can define a small number of singular points on an aerodynamic surface and in the flow which can be combined in various ways to create the structures and characterize the physical mechanisms of three-dimensional separated flows. This topological development is based on the hypothesis that vector fields of skin-friction lines and external streamlines remain continuous. Among examples treated are the lee-side separated flows about slender bodies at angle of attack with symmetric or asymmetric wake structures; about a protuberance normal to a wall; and over a rearward-facing axisymmetric step.

Tobak, M.↗
NASA NTRS2000

New Developments in Quaternion Estimation from Vector Observations

This paper contains a critical comparison of estimators minimizing Wahba's loss function. Some new results are presented for the QUaternion ESTimator (QUEST) and EStimators of the Optimal Quaternion (ESOQ and ESOQ2) to avoid the computational burden of sequential rotations in these algorithms. None of these methods is as robust in principle as Davenport's q method or the Singular Value Decomposition (SVD) method, which are significantly slower. Robustness is only an issue for measurements with widely differing accuracies, so the fastest estimators, the modified ESOQ and ESOQ2, are well suited to sensors that track multiple stars with comparable accuracies. More robust forms of ESOQ and ESOQ2 are developed that are intermediate in speed.

Markley, F. Landis↗
NASA NTRS1992

Dynamic Forms and Their Application to Control

The rigid body model plays a basic role in both mod- and control of many systems, including aircraft flight control. The distinctive feature of the rigid body is that its motion evolves on a curved space, Consequently, the designer must take into account the deterioration of chosen coordinations near their singularities. In these regions the control actions and the sensitivity to modeling and sensor errors become unacceptable. Thus, coordinate patches and patching logic should be a part of the overall control law design and implementation. The various dynamic forms, such as scalar forms, vector forms, matrix forms, rotational forms, Euler angle forms, and Euler parameter forms, described in the paper provide an effective means for coordinate patching and control law implementation. The utility of these forms is illustrated by means of several applications to flight control.

Meyer, George↗
NASA NTRS2008

Integrating the Gradient of the Thin Wire Kernel

A formulation for integrating the gradient of the thin wire kernel is presented. This approach employs a new expression for the gradient of the thin wire kernel derived from a recent technique for numerically evaluating the exact thin wire kernel. This approach should provide essentially arbitrary accuracy and may be used with higher-order elements and basis functions using the procedure described in [4].When the source and observation points are close, the potential integrals over wire segments involving the wire kernel are split into parts to handle the singular behavior of the integrand [1]. The singularity characteristics of the gradient of the wire kernel are different than those of the wire kernel, and the axial and radial components have different singularities. The characteristics of the gradient of the wire kernel are discussed in [2]. To evaluate the near electric and magnetic fields of a wire, the integration of the gradient of the wire kernel needs to be calculated over the source wire. Since the vector bases for current have constant direction on linear wire segments, these integrals reduce to integrals of the form

Champagne, Nathan J.↗
NASA NTRS1987

Quaternions as astrometric plate constants

A new method for solving problems in relative astrometry is proposed. In it, the relationship between the measured quantities and the components of the position vector of a star is modeled using quaternions, in effect replacing the plate constants of a standard four-plate-constant solution with the four components of a quaternion. The method allows a direct solution for the position vectors of the stars, and hence for the equatorial coordinates. Distortions, magnitude, and color effects are readily incorporated into the formalism, and the method is directly applicable to overlapping-plate problems. The advantages of the method include the simplicity of the resulting equations, their freedom from singularities, and the fact that trigonometric functions and tangential point transformations are not needed to model the plate material. A global solution over the entire sky is possible.

Jefferys, William H.↗
NASA NTRS1990

Optimal impulsive time-fixed orbital rendezvous and interception with path constraints

Minimum-fuel, impulsive, time-fixed solutions are obtained for the problem of orbital rendezvous and interception with interior path constraints. Transfers between coplanar circular orbits in an inverse-square gravitational field are considered, subject to a circular path constraint representing a minimum or maximum permissible orbital radius. Primer vector theory is extended to incorporate path constraints. The optimal number of impulses, their times and positions, and the presence of initial or final coasting arcs are determined. The existence of constraint boundary arcs and boundary points is investigated as well as the optimality of a class of singular arc solutions. To illustrate the complexities introduced by path constraints, an analysis is made of optimal rendezvous in field-free space subject to a minimum radius constraint.

Taur, D.-R.↗
NASA NTRS1993

Attitude control with realization of linear error dynamics

An attitude control law is derived to realize linear unforced error dynamics with the attitude error defined in terms of rotation group algebra (rather than vector algebra). Euler parameters are used in the rotational dynamics model because they are globally nonsingular, but only the minimal three Euler parameters are used in the error dynamics model because they have no nonlinear mathematical constraints to prevent the realization of linear error dynamics. The control law is singular only when the attitude error angle is exactly pi rad about any eigenaxis, and a simple intuitive modification at the singularity allows the control law to be used globally. The forced error dynamics are nonlinear but stable. Numerical simulation tests show that the control law performs robustly for both initial attitude acquisition and attitude control.

Paielli, Russell A.↗
NASA NTRS1982

Topology of three-dimensional separated flows

A Legendre formulation for a pattern of streamlines adjacent to a surface considered as trajectories with properties consistent with those of a constant vector field is used to develop a mathematical framework for three-dimensional separated flows. Convergence of skin-friction lines onto a particular skin-friction line originating from a particular saddle point is defined as a necessary condition for flow separation. Steady, three-dimensional flow is considered, and singular points occurring in the skin-friction lines are shown to happen where the skin friction or the surface vorticity become zero, and become nodal or saddle points. The separation initiates and continues only globally, as a mixture of an infinite set of friction lines, or locally, with one line. The topography of streamlines in two-dimensional sections of three-dimensional flows is discussed, and examples are provided of a round-nosed body of revolution at varying angles of attack.

Tobak, M.↗
NASA NTRS1993

Robust nonlinear control of vectored thrust aircraft

An interdisciplinary program in robust control for nonlinear systems with applications to a variety of engineering problems is outlined. Major emphasis will be placed on flight control, with both experimental and analytical studies. This program builds on recent new results in control theory for stability, stabilization, robust stability, robust performance, synthesis, and model reduction in a unified framework using Linear Fractional Transformations (LFT's), Linear Matrix Inequalities (LMI's), and the structured singular value micron. Most of these new advances have been accomplished by the Caltech controls group independently or in collaboration with researchers in other institutions. These recent results offer a new and remarkably unified framework for all aspects of robust control, but what is particularly important for this program is that they also have important implications for system identification and control of nonlinear systems. This combines well with Caltech's expertise in nonlinear control theory, both in geometric methods and methods for systems with constraints and saturations.

Doyle, John C.↗
NASA NTRS1975

An optimal control of a flexible spinning satellite

A modification of optimal spinning satellite control theory is proposed, based on introducing an additional vector into the equation for control torque components. This modification essentially means that the amplitudes of the time-dependent satellite perturbation functions can be made small when the amplitudes of the control torque components are allowed to be different. An algorithm for computer simulation of the satellite control theory is provided. A singular perturbation scheme is used which greatly reduces the number of degrees of freedom in the flexible satellite motion equations.

Das, A.↗