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At least 469 records · Page 26
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NASA NTRS1987

The pEst version 2.1 user's manual

This report is a user's manual for version 2.1 of pEst, a FORTRAN 77 computer program for interactive parameter estimation in nonlinear dynamic systems. The pEst program allows the user complete generality in definig the nonlinear equations of motion used in the analysis. The equations of motion are specified by a set of FORTRAN subroutines; a set of routines for a general aircraft model is supplied with the program and is described in the report. The report also briefly discusses the scope of the parameter estimation problem the program addresses. The report gives detailed explanations of the purpose and usage of all available program commands and a description of the computational algorithms used in the program.

Murray, James E.↗
NASA NTRS1987

Dynamic analysis of satellites with deployable hinged appendages

The nonlinear equations of motion determining the planar dynamical behavior of an orbiting satellite deploying both one and two rigid appendages have been formulated using Lagrange's equations. The analysis accounts for large angle rotations, Coriolis effects, and the gravitational gradient, and the resulting coupled governing equations are integrated numerically. The analysis is applied to the Space Shuttle based deployment of rigid truss-like members, and results show that spacecraft inertia parameters, appendage mass and length, deployment velocity, and initial conditions all influence the system response. It is found that the resulting librational movement is related to the size of the deployment payload, and that gravitational forces lead to vehicle stabilization.

Oakes, Kevin F.↗
NASA NTRS1988

Minimum-Time Control For Robotic Manipulators

Existence theorem proved for nonlinear systems. Report discusses mathematical requirements for existence of solution to minimum-time control problem for robotic manipulator that obeys nonlinear equations of motion.

Wen, John T.↗
NASA NTRS1988

Accurate boundary conditions for exterior problems in gas dynamics

The numerical solution of exterior problems is typically accomplished by introducing an artificial, far field boundary and solving the equations on a truncated domain. For hyperbolic systems, boundary conditions at this boundary are often derived by imposing a principle of no reflection. However, waves with spherical symmetry in gas dynamics satisfy equations where incoming and outgoing Riemann variables are coupled. This suggests that natural reflections may be important. A reflecting boundary condition is proposed based on an asymptotic solution of the far field equations. Nonlinear energy estimates are obtained for the truncated problem and numerical experiments presented to validate the theory.

Hagstrom, Thomas↗
NASA NTRS1988

MHOST: An efficient finite element program for inelastic analysis of solids and structures

An efficient finite element program for 3-D inelastic analysis of gas turbine hot section components was constructed and validated. A novel mixed iterative solution strategy is derived from the augmented Hu-Washizu variational principle in order to nodally interpolate coordinates, displacements, deformation, strains, stresses and material properties. A series of increasingly sophisticated material models incorporated in MHOST include elasticity, secant plasticity, infinitesimal and finite deformation plasticity, creep and unified viscoplastic constitutive model proposed by Walker. A library of high performance elements is built into this computer program utilizing the concepts of selective reduced integrations and independent strain interpolations. A family of efficient solution algorithms is implemented in MHOST for linear and nonlinear equation solution including the classical Newton-Raphson, modified, quasi and secant Newton methods with optional line search and the conjugate gradient method.

Nakazawa, S.↗
NASA NTRS1987

Optimal time free nodal transfers between elliptical orbits

The paper presents the necessary conditions for the minimum fuel, time-free transfer between two noncoplanar elliptical orbits. It is shown that the solution is obtained by solving a system of three nonlinear equations for three unknowns. The case where the impulses are applied along the line of nodes is discussed. In general, this nodal transfer is nonoptimal, but the characteristic velocity for the best nodal transfer, called the minimizing nodal transfer, is reasonably close to the one for the optimal transfer for it to be useful as a substitute for a practical transfer. Furthermore, when the relative position of the two terminal orbits is varied, the two characteristic velocities, for the minimizing nodal transfer and the optimal transfer, exhibit the same trend in the sense that they pass through their maxima and minima at nearly the same relative position. This makes the set of explicit formulas for computing the minimizing nodal transfer, as presented in this paper, a useful tool for designing a minimum fuel transfer between several orbits.

Vinh, Nguyen X.↗
NASA NTRS1988

Preliminary Orbit Determination System (PODS) for Tracking and Data Relay Satellite System (TDRSS)-tracked target Spacecraft using the homotopy continuation method

The Preliminary Orbit Determination System (PODS) provides early orbit determination capability in the Trajectory Computation and Orbital Products System (TCOPS) for a Tracking and Data Relay Satellite System (TDRSS)-tracked spacecraft. PODS computes a set of orbit states from an a priori estimate and six tracking measurements, consisting of any combination of TDRSS range and Doppler tracking measurements. PODS uses the homotopy continuation method to solve a set of nonlinear equations, and it is particularly effective for the case when the a priori estimate is not well known. Since range and Doppler measurements produce multiple states in PODS, a screening technique selects the desired state. PODS is executed in the TCOPS environment and can directly access all operational data sets. At the completion of the preliminary orbit determination, the PODS-generated state, along with additional tracking measurements, can be directly input to the differential correction (DC) process to generate an improved state. To validate the computational and operational capabilities of PODS, tests were performed using simulated TDRSS tracking measurements for the Cosmic Background Explorer (COBE) satellite and using real TDRSS measurements for the Earth Radiation Budget Satellite (ERBS) and the Solar Mesosphere Explorer (SME) spacecraft. The effects of various measurement combinations, varying arc lengths, and levels of degradation of the a priori state vector on the PODS solutions were considered.

Kirschner, S. M.↗
NASA NTRS1989

Dynamics of articulated structures

An articulated structure is defined as an assembly of flexible bodies that may be coupled by kinematic connections and force elements that permit large relative displacement and rotation. Kinematics of such systems is defined using one reference frame for each body in the system and deformation modal coordinates that define displacement fields within flexible bodies. Deformation kinematics are defined by both elastic vibration and static correction deformation modes. Linear elastic deformation is presumed; i.e., a linear stress-strain relation is valid and relative displacements within each elastic component are small enough so that the theory of linear elasticity applies. Coupling of reference and modal coordinates leads to a system of nonlinear equations of motion. Methods of automatically generating and solving these equations of motion are outlined.

Haug, Edward J.↗
NASA NTRS1989

Analytic theory for the selection of 2-D needle crystal at arbitrary Peclet number

An accurate analytic theory is presented for the velocity selection of a two-dimensional needle crystal for arbitrary Peclet number for small values of the surface tension parameter. The velocity selection is caused by the effect of transcendentally small terms which are determined by analytic continuation to the complex plane and analysis of nonlinear equations. The work supports the general conclusion of previous small Peclet number analytical results of other investigators, though there are some discrepancies in details. It also addresses questions raised on the validity of selection theory owing to assumptions made on shape corrections at large distances from the tip.

Tanveer, Saleh↗
NASA NTRS1987

Control of Spacecraft Control Laboratory Experiment (SCOLE) slew maneuvers

This is the second report of a set of two reports on the dynamics and control of slewing maneuvers of NASA Spacecraft Control Laboratory Experiment (SCOLE). The control problem of slewing maneuvers of SCOLE is developed in terms of an arbitrary maneuver about any given axis. The control system is developed for the combined problem of rigid-body slew maneuver and vibration suppression of flexible appendage. The control problem is formulated by incorporating the nonlinear equations derived in the previous report and is expressed in terms of a two-point boundary value problem utilizing a quadratic type of performance index. The two-point boundary value problem is solved as a hierarchical control problem with the overall system being split in terms of two subsystems, namely the slewing of the entire assembly and the vibration suppression of the flexible antenna. The coupling variables between the two dynamical subsystems are identified and these two subsystems for control purposes are treated independently in parallel at the first level. Then the state-space trajectory of the combined problem is optimized at the second level.

Kakad, Y. P.↗
NASA NTRS1988

Current driven instabilities of an electromagnetically accelerated plasma

A plasma instability that strongly influences the efficiency and lifetime of electromagnetic plasma accelerators was quantitatively measured. Experimental measurements of dispersion relations (wave phase velocities), spatial growth rates, and stability boundaries are reported. The measured critical wave parameters are in excellent agreement with theoretical instability boundary predictions. The instability is current driven and affects a wide spectrum of longitudinal (electrostatic) oscillations. Current driven instabilities, which are intrinsic to the high-current-carrying magnetized plasma of the magnetoplasmadynmic (MPD) accelerator, were investigated with a kinetic theoretical model based on first principles. Analytical limits of the appropriate dispersion relation yield unstable ion acoustic waves for T(i)/T(e) much less than 1 and electron acoustic waves for T(i)/T(e) much greater than 1. The resulting set of nonlinear equations for the case of T(i)/T(e) = 1, of most interest to the MPD thruster Plasma Wave Experiment, was numerically solved to yield a multiparameter set of stability boundaries. Under certain conditions, marginally stable waves traveling almost perpendicular to the magnetic field would travel at a velocity equal to that of the electron current. Such waves were termed current waves. Unstable current waves near the upper stability boundary were observed experimentally and are in accordance with theoretical predictions. This provides unambiguous proof of the existence of such instabilites in electromagnetic plasma accelerators.

Chouetri, E. Y.↗
NASA NTRS1988

Accurate boundary conditions for exterior problems in gas dynamics

The numerical solution of exterior problems is typically accomplished by introducing an artificial, far-field boundary and solving the equations on a truncated domain. For hyperbolic systems, boundary conditions at this boundary are often derived by imposing a principle of no reflection. However, waves with spherical symmetry in gas dynamics satisfy equations where incoming and outgoing Riemann variables are coupled. This suggests that natural reflections may be important. A reflecting boundary condition is proposed based on an asymptotic solution of the far-field equations. Nonlinear energy estimates are obtained for the truncated problem and numerical experiments presented to validate the theory.

Hagstrom, Thomas↗
NASA NTRS1988

Relationships between near-surface plankton concentrations, hydrography, and satellite-measured sea surface temperature

Sea surface temperatures (SSTs) mapped by IR satellite images and in situ hydrographic measurements off the west coast of British Columbia for early-winter and midsummer periods were correlated with in situ measurements of surface chlorophyll and zooplankton concentration. Correlations between winter log(e) transformed zooplankton concentrations and SSTs demonstrated that IR satellite imagery could explain 49 percent of the sampled zooplankton concentration variance. A least-squares-fit nonlinear equation showed that satellite-measured SST patterns explained 72 percent of the log(e) transformed chlorophyll variance. However, summer zooplankton concentrations were not consistently related to satellite temperature patterns.

Thomas, A. C.↗
NASA NTRS1989

Inclusion of filter modulation in synthetic-discriminant-function construction

A technique in which the filter modulation is included in the synthesis of a synthetic-discriminant-function (SDF) matched spatial filter is presented. In the filter synthesis, a system of simultaneous nonlinear equations is solved with an iteration procedure. A computer simulation of the new method using thresholded images of the Space Shuttle over a range of aspect angles was performed for phase-only filters (POFs) and binary-phase-only filters (BPOFs). The filters constructed are capable of obtaining the specified peak-correlation response to within 1 percent with a high signal-to-clutter-ratio for the one-class problem, the two-class problem, and the multilevel problem. In contrast, conventional projection SDF POFs and BPOFs are unable to produce the desired peak-correlation response.

Jared, David A.↗
NASA NTRS1989

Model and simulation development for turbopump health monitoring by parameter estimation

The nonlinear equations describing the flow, pressure and temperature dynamics of the High Pressure Fuel Turbopump of the Space Shuttle Main Engine are summarized and implemented in a digital simulation. Some closed form approximations to the operating curves of the turbopump are made so that closed form derivatives exist. These equations and approximations are then used to develop an extended Kalman filter that estimates the dynamic states of the turbopump and a parameter that can reflect turbopump degradation. The filter is implemented as a digital computer program and applied to data generated by the digital simulation of the turbopump with substantial noise added to the output signals. The results indicate that the parameter estimate converges quickly and accurately. This suggests that the parameter estimate can be used to monitor for turbopump degradations affecting its value.

Walker, Bruce K.↗
NASA NTRS1989

The application of TSIM software to act design and analysis on flexible aircraft

The TSIM software is described. This is a package which uses an interactive FORTRAN-like simulation language for the simulation on nonlinear dynamic systems and offers facilities which include: mixed continuous and discrete time systems, time response calculations, numerical optimization, automatic trimming of nonlinear aircraft systems, and linearization of nonlinear equations for eigenvalues, frequency responses and power spectral response evaluation. Details are given of the application of TSIM to the analysis of aeroelastic systems under the RAE Farborough extension FLEX-SIM. The aerodynamic and structural data for the equations of motion of a flexible aircraft are prepared by a preprocessor program for incorporation in TSIM simulations. Within the simulation, the flexible aircraft model may then be selected interactively for different flight conditions and modal reduction techniques applied. The use of FLEX-SIM is demonstrated by an example of the flutter prediction for a simple aeroelastic model. By utilizing the numerical optimization facility of TSIM, it is possible to undertake identification of required parameters in the TSIM model within the simulation.

Kaynes, Ian W.↗
NASA NTRS1989

Spatial evolution of nonlinear acoustic mode instabilities on hypersonic boundary layers

The effects are considered of strong critical layer nonlinearity on the spatial evolution of an initially linear acoustic mode instability wave on a hypersonic flat plate boundary layer. The analysis shows that nonlinearity, which is initially confined to a thin critical layer, first becomes important when the amplitude of the pressure fluctuations become 0(1/M exp 4 In M exp 2), where M is the free stream Mach number. The flow outside the critical layer is still determined by linear dynamics and therefore takes the form of a linear instability wave, but with its amplitude completely determined by the flow within the critical layer. The latter flow is determined by a coupled set of nonlinear equations, which were solved numerically.

Goldstein, M. E.↗