In memoriam Julius Bartels

Ohne Zusammenfassung

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In memoriam Julius Bartels

     

A New Mathematical Formulation for Strapdown Inertial Navigation

A differential equation is developed for the orientation vector relating the body frame to a chosen reference frame. The time derivative of this vector is the sum of the inertially measurable angular velocity vector and of the inertially nonmeasurable noncommutativity rate vector. It is precisely this noncommutativity rate vector that causes the computational problems when numerically integrating the direction cosine matrix. The orientation vector formulation allows the noncommutativity contribution to be isolated and, therefore, treated separately and advantageously. An orientation vector mechanization is presented for a strap down inertial system. Further, an example is given of the applica tion of this formulation to a typical rigid body rotation problem.     

Analysis of a Class of Nonlinear Sampled-Data Systems with a Gaussian Input Signal

The problem treated here is the analysis of a class of nonlinear sampled-data systems with a Gaussian input signal. The nonlinear element is a symmetrical limiter (memoryless device) that feeds the linear element. Preceding the limiter is a sampler and zero-order hold unit for data reconstruction. The analysis is predicated on finding an equivalent gain for the nonlinear element such that the mean-square error is a minimum. The nonlinearity is thus replaced by a linear component and the system is then analyzed by conventional techniques. It is also shown that for appropriate sampling rates the sampled-data system is equivalent to a continuous system due to the action of the sampler-hold combination. All calculations pertaining to the limiter input signal require the use of a transfer function that is interior to the feedback loop. However, in developing this transfer function, the overall system is considered so that the system output may be evaluated after the value of equivalent gain has been found.     

On Optimal Allocation and Guidance Laws for Linear lnterception and Rendezvous Problems

This paper considers the problem of guiding N interceptors so that they intercept or rendezvous with N targets at the same time T. It is assumed that the interceptors and targets are described by linear time-varying differential equations (deterministic or stochastic). Under certain assumptions both the optimal (static or dynamic) interceptor-target allocation and the guidance of each interceptor for the optimal allocation can be obtained with modest real-time and storage computer requirements.     

Target-Handling Capacity of a Phased-Array Tracking Radar

The factors which affect the target-handling capacity of an agile-beamelectronically scanned multitarget-tracking radar are reviewed and analyze.Consideration is given to the choice of strategy for dwell allocation amongtargets, the choice of trajectory extrapolation algorithms for target tracking, and the determination of saturation target acquisition rates. Emphasisis placed upon radar systems with control computers having limited speed and memory, and recommendations are made for allocation strategy and targetytracking algorithms, based on uniform sampling, to be used in maximizing thetarget-handling capacity in this situation.     

Stable mid-latitude red arcs: Observations and theory

Summary The observational features of the arc are fairly well established. At present, the thermal conduction model appears to explain the red arc features most consistently, but it must be noted that a soft electron flux would give very similar results. Ion temperature measurements in the vicinity of an arc, which should be forthcoming in the very near future, can establish conclusively whether transverse electric fields play any important role in the formation of the arcs. Accepting the assumption that the arcs are the result of energy flowing down from the plasmasphere, the major remaining question is: where does the energy come from and how does it get into the plasmasphere? The various proposed mechanisms discussed in the previous chapter appear feasible, but much work needs to be done before this problem is completely resolved.On leave from the Department of Electrical Engineering, The University of Michigan, Ann Arbor.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Some Comments on the Dynamics of Urban Structural Development

The suggestion is made that the aerospace industry examine the dynamics of urban structural development, that it identify the forces which act on the elements comprising the structure of the city, and that it describe the relationship between and the relative movements of those elements. By formulating such a general theory of urban structural development, urban political, social, and economic leadership may be given the means by which permanent remedies?including technological?may be devised and applied. This paper presents examples of such means and explains their application and effects.     

High-Speed Homopolar Inductor Alternators of Minimum Leakage Reactance

The leakage reactance of the machine is expressed as an equation involving slot leakage, end-connection leakage, differential leakage, stator-halves leakage, and tooth-top leakage reactance. This leakage reactance equation, or objective function, is then minimized under suitable constraints. Geometric programming is used to carry through the optimization procedure. A computer program is developed and applied to find the optimum leakage reactance for a 95 kVA, 208 V, wye-connected, 40 800 r/min aerospace alternator, using 8-, 10-, and 12-pole machines.     

Logistics Transportation for Space Station Support

Logistics support of a long duration space station will dictate a high degree of space flight activity to rotate personnel and transport supplies and equipment. Systems characteristics and mission requirements for space station logistics have been analyzed within the context of a broad spectrum of space missions. Preliminary concepts for a space shuttle system (space transportation) have been developed. This system can support not only a space station program, but a wide variety of space missions for both NASA and the DOD.     

Atmospheric Error in Range and Range-Rate Measurements between a Ground Station and an Artificial Satellite

The propagation errors caused by the atmosphere are investigated in order to find out the causes of the observed errors in range and range-rate measurements between a ground station and an artificial satellite. The calculations show that the observed errors are mostly caused by the measuring instruments. The propagation errors are mainly caused by increases, decreases, or fluctuations of the refractive index of the atmosphere, and the errors caused by the refraction of the propagation path are about 10 percent of the errors caused by the decrease of the propagation velocity. The tropospheric range errors are less than 150 meters and are approximately expressed by a cotangent function, and they are reduced by about 90 percent through the use of monthly average refractivity profiles of the troposphere. The ionospheric errors are usually negligible at centimeter radio waves (less than 10 cm), and even at decimeter waves or meter waves almost all errors can be removed by the use of two different frequencies on the down-link so that the range can be made independent of frequency.