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Stability analysis parameter plane technique for tactical missile control system design, correlating variable parameters with characteristic equation roots location
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In theories of numerical stability, roots to a characteristic polynomial are sought, which, in the case of the predictor with iterative correction method of numerical integration, are eigenvalues of a matrix whose elements depend on the coefficients used in the integration process. The characteristic polynomial is displayed explicitly in terms of the elements of the characteristic matrix.
Upon resupply of exogenous nitrogen to nitrogen-stressed plants, uptake rate of nitrogen is enhanced relative to nonstressed plants. Absorption of nitrogen presumably is dependent on availability of carbohydrates in the roots. A buildup in soluble carbohydrates thus should occur in roots of nitrogen-stressed plants, and upon resupply of exogenous nitrogen the increased uptake rate should be accompanied by a rapid decline in carbohydrates to prestress levels. To evaluate this relationship, three sets of tobacco plants growing in a complete hydroponic solution containing 1.0 mM NO3- were either continued in the complete solution for 21 d, transferred to a minus-nitrogen solution for 21 d, or transferred to a minus-nitrogen solution for 8-9 d and then returned to the 1.0 mM NO3- solution. These nitrogen treatments were imposed upon plants growing at photosynthetic photon flux densities of 700 and 350 micromoles m-2 s-1. Soluble carbohydrate levels in roots increased during onset of nitrogen stress to levels that were fourfold greater than in roots of non-stressed plants. Following resupply of external nitrogen, a rapid resumption of nitrogen uptake was accompanied by a decline in soluble carbohydrates in roots to levels characteristic of nonstressed plants. This pattern of soluble carbohydrate levels in roots during onset of and recovery from nitrogen stress occurred at both irradiance levels. The response of net photosynthetic rate to nitrogen stress could be expressed as a nonlinear function of concentration of reduced nitrogen in leaves. The net photosynthetic rate at a given concentration of reduced nitrogen, however, averaged 10% less at the lower than at the higher irradiance. The decline in net photosynthetic rate per unit of reduced nitrogen in leaves at the lower irradiance was accompanied by an increase in the nitrate fraction of total nitrogen in leaves from 20% at the higher irradiance to 38% at the lower irradiance.
The interdependence of root and shoot growth produces a functional equilibrium as described in quantitative terms by numerous authors. It was noted that bean seedlings grown in a constant environment tended to have a constant distribution pattern of dry matter between roots and leaves characteristic of the set of environmental conditions. Disturbing equilibrium resulted in a change in relative growth of roots and leaves until the original ratio was restored. To define a physiological basis for regulation of nitrogen uptake within the balance between root and shoot activities, the authors combined a partioning scheme and a utilization priority assumption in which: (1) all carbon enters the plant through photosynthesis in leaves and all nitrogen enters the plant through active uptake by roots, (2) nitrogen uptake by roots and secretion into the xylem for transport to the shoots are active processes, (3) availability of exogenous nitrogen determines concentration of soluble carbohydrates within the roots, (4) leaves are a source and a sink for carbohydrates, and (5) the requirement for nitrogen by leaf growth is proportionally greater during initiation and early expansion than during later expansion.
It is beneficial to use a distributed parameter model for large space structures because the approach minimizes the number of model parameters. Holzer's transfer matrix method provides a useful means to simplify and standardize the procedure for solving the system of partial differential equations. Any large space structures can be broken down into sub-structures with simple elastic and dynamical properties. For each single element, such as beam, tether, or rigid body, we can derive the corresponding transfer matrix. Combining these elements' matrices enables the solution of the global system equations. The characteristics equation can then be formed by satisfying the appropriate boundary conditions. Then natural frequencies and mode shapes can be determined by searching the roots of the characteristic equation at frequencies within the range of interest. This paper applies this methodology, and the maximum likelihood estimation method, to refine the modal characteristics of the NASA Mini-Mast Truss by successively matching the theoretical response to the test data of the truss. The method is being applied to more complex configurations.
The problem of calculating the temperature distribution in an insulated slab is investigated. Exact and approximate solutions are obtained, and the results are compared to determine the ranges of applicability of the approximations. The approximations are found to be within 5 percent of the exact solution when the ratio of the thermal capacitance of the metal to that of the insulation and the ratio of the conductance of the metal to that of the insulation are sufficiently large. The roots of the characteristic equation of the exact solution are generally applicable to the two-slab heat-transfer problem and are tabulated up to the first nine roots.
Sixteen point probes monitored moisture level in the root medium of the wheat plants grown in greenhouse SVET on the MIR/NASA space science program. The article outlines types of water migration in the absence of gravity. Hydrophysical characteristics of perspective root media have been explored. Results of the water supply monitoring and control in the course of experiment are reported. The authors put forward porous root media to facilitate water migration and aeration.
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A characteristic feature of the Fourier Power Density Spectrum (PDS) observed from black hole X-ray binaries in low/hard and intermediate spectral states is a broad band-limited noise, characterized by a constant below some frequency (a "break" frequency) and a power law above this frequency. It has been shown that the variability of this type can be produced by the inward diffusion of the local driving perturbations in a bounded configuration (accretion disk or corona). In the framework of this model, the perturbation diffusion time to is related to the phenomenological break frequency, while the PDS power-law slope above the "break" is determined by the viscosity distribution over the configuration. The perturbation diffusion scenario explains the decay of the power of X-ray variability observed in a number of compact sources (containing black hole and neutron star) during an evolution of theses sources from low/hard to high/soft states. We compare the model predictions with the subset of data from Cyg X-1 collected by the Rossi X-ray Time Explorer (RXTE). Our extensive analysis of the Cyg X-1 PDSs demonstrates that the observed integrated power P(sub x), decreases approximately as a square root of the characteristic frequency of the driving oscillations v(sub dr). The RXTE observations of Cyg X-1 allow us to infer P(sub dr), and t(sub o) as a function of v(sub dr). We also apply the basic parameters of observed PDSs, power-law index and low frequency quasiperiodic oscillations. to infer Reynolds (Re) number from the observations using the method developed in our previous paper. Our analysis shows that Re-number increases from values about 10 in low/hard state to that about 70 during the high/soft state. Subject headings: accretion, accretion disks-black hole physics-stars:individual (Cyg X-1) :radiation mechanisms: nonthermal-physical data and processes
Control-configured vehicle technology has increased the demand for detailed analysis of dynamic stability and control, handling and ride qualities, and control system dynamics at early stages of preliminary design. An approximate, but reasonably accurate, set of equations of motion are needed for these early analyses. Such a formulation is developed for the longitudinal dynamics of elastic airplanes. It makes use of only rigid-body aerodynamic stability derivatives in formulating the forces and moments due to elastic motion. Verification of accuracy using data for the B-1 airplane shows very good agreement. Frequencies and damping ratios of the coupled modes corresponding to complex roots of the characteristic equations agree closely with four symmetric elastic modes included.
Control-configured vehicle technology has increased the demand for detailed analysis of dynamic stability and control, handling and ride qualities, and control system dynamics at early stages of preliminary design. An approximate but reasonably accurate set of equations of motion are needed for these early analyses. Such a formulation is developed for the longitudinal dynamics of elastic airplanes. It makes use of only rigid-body aerodynamic stability derivatives in formulating the forces and moments due to elastic motion. Verification of accuracy using data for the B-1 airplane shows very good agreement. Frequencies and damping ratios of the coupled modes corresponding to complex roots of the characteristic equations agree closely with four symmetric elastic modes included.
An analytic solution for the J2 perturbed equatorial orbit is obtained in terms of elliptic functions and integrals. The necessary equations for computing the position and elocity vectors, and the time are given in terms of known functions. The perturbed periapsis and apoapsis distances are determined from the roots of a characteristic cubic.
The problem of the reduction of the radar cross section (RCS) of open-ended cavities was studied. The issues investigated were reduction through lossy coating materials on the inner cavity wall and reduction through shaping of the cavity. A method was presented to calculate the RCS of any arbitrarily shaped structure in order to study the shaping problem. The limitations of this method were also addressed. The modal attenuation was studied in a multilayered coated waveguide. It was shown that by employing two layers of coating, it was possible to achieve an increase in both the magnitude of attenuation and the frequency band of effectiveness. The numerical method used in finding the roots of the characteristic equation breaks down when the coating thickness is very lossy and large in terms of wavelength. A new method of computing the RCS of an arbitrary cavity was applied to study the effects of longitudinal bending on RCS reduction. The ray and modal descriptions for the fields in a parallel plate waveguide were compared. To extend the range of validity of the Shooting and Bouncing Ray (SBR) method, the simple ray picture must be modified to account for the beam blurring.
The concept of dividing random processes into classes (e.g., stationary, locally stationary, periodically correlated, and harmonizable) has long been employed. A new class of random processes is introduced which includes many of these processes as well as other interesting processes which fall into none of the above classes. Such random processes are denoted as linearly correlated. This class is shown to include the familiar stationary and periodically correlated processes as well as many other, both harmonizable and non-harmonizable, nonstationary processes. When a process is linearly correlated for all t and harmonizable, its two-dimensional power spectral density S(x)(omega 1, omega 2) is shown to take a particularly simple form, being non-zero only on lines such that omega 1 to omega 2 = + or - r(k) where the r(k's) are (not necessarily equally spaced) roots of a characteristic function. The relationship of such processes to the class of stationary processes is examined. In addition, the application of such processes in the analysis of typical helicopter noise signals is described.
This paper summarizes the development of the methods and a computer program to compute the probability of instability of a dynamic system than can be represented by a system of second-order ordinary linear differential equations. Two instability criteria based upon the roots of the characteristics equation or Routh-Hurwitz test functions are investigated. Computational methods based on system reliability analysis methods and importance sampling concepts are proposed to perform efficient probabilistic analysis. Numerical examples are provided to demonstrate the methods.
The concept of dividing random processes into classes (e.g., stationary, locally stationary, periodically correlated, and harmonizable) has long been employed. A new class of random processes is introduced which includes many of these processes as well as other interesting processes which fall into none of the above classes. Such random processes are denoted as linearly correlated. This class is shown to include the familiar stationary and periodically correlated processes as well as many other, both harmonizable and non-harmonizable, nonstationary processes. When a process is linearly correlated for all t and harmonizable, its two-dimensional power spectral density S(x) (omega 1, omega 2) is shown to take a particularly simple form, being non-zero only on lines such that omega 1 to omega 2 = + or - r(k) where the r(k's) are (not necessarily equally spaced) roots of a characteristic function. The relationship of such processes to the class of stationary processes is examined. In addition, the application of such processes in the analysis of typical helicopter noise signals is described.
In the determination of the performance of an air-cooled turbine, the cooling-air-flow characteristics between the root and the tip of the blades must be evaluated. The methods, which must be verified and the unknown functions evaluated, that are expected to permit the determination of pressure, temperature, and velocity through the blade cooling-air passages from specific investigation are presented.