A uniform method (with respect to the type of the conic section) for solving the Lambert boundary value problem is presented. It is derived by using the KS-transformation and consists in solving one nonlinear equation. It can be used either in the ordinary x-frame (physical space) as well as in the KS-coordinates (regularized space).

Methods for solving boundary-value problems in astrodynamics are developped and applied to interplanetary transfer- and flyby-trajectories.

A new uniform method (with respect to the type of the conic section) for the classical Lambert Problem is presented and results in the solution of one nonlinear equation only. The uniformly valid state-transition matrix of the Keplerian motion is established by means of the KS-transformation.

Perturbed boundary-value problems are treated by integrating the perturbed trajectory numerically and by performing the differential correction technique using the analytical state-transition matrix of the unperturbed motion. Feasibility and efficiency of this procedure are demonstrated by several realistic, in part strongly perturbed and ill-conditioned transfer- and fly-by-trajectories.

ZUSAMMENFASSUNG

Unter einem astrodynamischen Randwertproblem versteht man die Bestimmung der Bahn eines Mobils im Gravitationsfeld (des Sonnensystems), sodass sie gewisse vorgeschriebene Bedingungen erfullt. Zur Behandlung dieses komplexen Problems werden in der vorliegenden Arbeit theoretische Methoden untersucht und entwickelt. Es werden semi-numerische Verfahren erarbeitet und auf die Berechnung von realistischen interplanetaren Transfer- und Flyby-Bahnen angewandt. Dabei zeigt sich eine deutliche Verbesserung und Abkürzung der Rechenzeit gegenüber klassischen numerischen Methoden.

Die Basis der Untersuchungen bildet die ungestörte Bewegung. Dieses analytisch lösbare Zweikörperproblem (Sonne - Mobil) wird zweckmässig mit Hilfe der Kunstaanheimo/Stiefel-Transformation behandelt. Durch Verwendung der sog. Stumpff-Funktionen erhält man eine uniform gültige, d.h. vom speziellen Bahntypus (elliptisch, parabolisch, hyperbolisch) unabhängige Lösung (Kap. 1.1).

Die Bahnberechnung einer interplanetaren Sonde, die ausgehend von der Erde einen Zielplaneten (unter eventuell nahem Vorbeiflug an einem Zwischenplaneten) erreichen und zusätzliche Randbedingungen erfüllen soll, wird in folgender Form gelöst:

a) Es wird eine Ausgangsnäherung ermittelt, indem die Bahn aus heliozentrischen ungestörten Keplerbogen zusammengesetzt wird (4.2). Die Bestimmung eines solchen Bogens erfordert die Lösung des sog. Lambert Problems, d.h. es ist eine Keplerbahn durch zwei Punkte mit vorgeschriebener Laufzeit zu konstruieren. Fur diese klassische Randwertaufgabe der Himmelsmechanik wird eine neue Lösungsmethode entwickelt, welche das Problem auf eine einzige nichtlineare algebraische Gleichung reduziert (1.2, und Literaturhinweis [6]).

b) Die heliozentrischen Bogen werden an den Flyby-Planeten durch planetozentrische Hyperbeln verknüpft (4.2). Für die Berechnung der approximativen Startgeschwindigkeit in einem gegebenen Punkt des Erdsystems, sodass eine Abflughyperbel mit vorgeschriebener asymptotischen Geschwindigkeit resultiert, wird eine allgemein gültige Lösungsformel hergeleitet (1.3).

c) Die zusätzlichen Nebenbedingungen werden differentiell durch Variation der Anfangswerte, resp. durch Unterwegs-Korrekturen befriedigt. Die dazu benötigte sog. Uebergangsmatrix wird mit Hilfe der KS-Transformation einfach hergeleitet und kompakt und uniform dargestellt (2). Mittels der kanonischen Mechanik wird auch die Inverse der KS-Uebergangsmatrix analytisch berechnet (2.1) und als Nebenresultat ergeben sich die Störungsgleichungen fur die Elemente der Keplerbahn (3.1).

d) Fur realistische Bahnberechnung müssen die Störungen der Planeten berücksichtigt werden. Statt die Übergangsmatrix durch rechenaufwendige numerische Integration der Variationsgleichungen, resp. benachbarter Bahnen, zu berechnen, machen wir den folgenden Versuch: Die Bahn wird zwar unter Berücksichtigung der Störungen numerisch integriert, fur ihre Verbesserung (Variation) benutzen wir jedoch die analytische Übergangsmatrix der ungestörten Bewegung (4.2). Dieses Vorgehen und seine Auswirkung auf die Konvergenz des iterativen (Newton-) Prozesses wird theoretisch untersucht (3.3) und an realistischen Beispielen der Weltraumfahrt getestet (5). Es erweist sich selbst bei schwierigen, stark gestorten Flyby-Problemen als erfolgreich und kostensparend (5.2).

In der Arbeit wird auch auf die auftretenden numerischen und programmiertechnischen Probleme eingegangen, z.B. auf die "Instabilität" der Iteration (3.3), die schlechte Kondition (3.3), die Berechnung von Stumpff-Funktionen (5.1), usw.

An dieser Stelle mochte ich Herrn Prof. Dr. E. Stiefel herzlich danken fur sein stetes Interesse, das er dieser Arbeit entgegengebracht hat, fur seine Unterstützung und viele Anregungen. Mein Dank geht auch an Herrn Prof. Dr. P. Läuchli fur die Übernahme des Korreferates und endlich an die Herren Dr. U. Kirchgraber und Dr. J. Nötzli fur viele anregende Diskussionen.

The uniform valid state transition matrix of the pure Keplerian motion is established by means of the KS-transformation. Perturbed interplanetary transfer- and flyby-problems are treated by integrating the perturbed trajectory numerically and by performing the differential correction technique using the analytical transition matrix of the unperturbed motion. Numerical examples show the efficiency of this procedure and the improvement of the computing time and accuracy in comparison with the shooting method.

The disadvantages of some frequently used techniques for approximating time delays are briefly discussed. It is shown that these difficulties do not exist when performing integration by means of a semianalytical integration method. This technique consists of expanding the state variables of a system in power series, while making use of analytical recursion formulas for the calculation of the coefficients of the series. By exploiting the analytical features of the power series method, time delay with fixed and variable delay times can be handled efficiently and accurately without any additional approximation. Two sample problems are solved using a new simulation package (the Power Series Continuous Simulation Program).

The paper deals with differential equations with discontinuous right-hand sides. The variational equations for the partial derivatives of the solution with respect to the initial values are established. Formulae for the jump in the partial derivatives at the points where the right-hand side is discontinuous are derived. An application to a two-point boundary value problem is given. The theory is extended to allow general variations and transformations of variables at the points of discontinuity.

This paper describes an extension of Pascal by coroutines as a basic tool to make quasi-parallel programming possible. This extension is acheived by predefined procedures, i.e. by semantical means without modification of the syntax of the language. Process and simulation concepts are developed entirely in the extended Pascal. These concepts are suited for quasi-parallel programming and for process-oriented simulation of discrete-event systems. The presented simulation system is easy to implement, it is flexible and modifiable. It retains the powerful facilities and the portability and availability of Pascal.

The performance of a symmetric multiprocessor system on the level of memory requests is studied. The multiprocessor consists of a number of identical processors, each having its local private memory and each being connected via a system of identical buses to all global memory modules. The system is modelled by a Markovian queueing network and solved approximately by a hierarchical decomposition technique. A closed-form solution for the steady-state probabilities is presented and its numerical properties are discussed. Formulas for computing various performance measures are included. Simple lower and upper bounds for the throughput are derived which converge to the exact value as the number of processors increases.

An engineering approach to functional design and specification of multilevel computer systems is presented. The overall system is designed as a hierarchy of abstract state machines and described in a MODULA-2 like language. Functions are defined either by input-output specification or operationally. Standard mathematical notation is applied as needed. This semiformal specification appears to be easy, concise, comprehensible and still precise enough to avoid ambiguous interpretation. The specification can be turned into an executable MODULA-2 program and hence used for fast prototyping. The approach is demonstrated by an extensive example based on a realized operating system kernel supporting quasi-parallel programming.

Analytical lower and upper bounds for the throughput of closed queueing networks with single and delay (infinite) serves are studied. The numerical evaluation of these bounds requires a small number of significant operations which is independent of the population N. The previously known balanced-job bounds are generalized to networks containing delay servers (terminals) and a hierarchy of bounds is obtained for single and multiple class networks. For the single class network, further new bounds are derived: lower and upper bounds that require the evaluation of one square root and an upper bound that requires a constant number of exponentiations. This upper bound does not employ the balancing of server loadings and is especially useful for asymtotic analysis in the case of a large number of customers N.

A class of advanced distributed process control systems is introduced. The presented systems are local area networks consisting of a large number of microprocessor-based computer nodes that perform control and monitoring functions. The computer nodes communicate by broadcasting state information in source-addressed messages. The potential advantages of this communication mechanism over conventional destination-addressed message passing are: no side effect of function executions, convenient monitoring of running systems, facilitation of incremental system construction and system extension while the system is in service, support of backward error tracing and the identification of fault sources. There already exist a few distributed process control systems that are based on broadcasting source-addressed messages. The technological progress in high-speed data transmission and further research in broadcast-oriented computer communication will broaden the application range of these systems.

The introduced systems are bus-structured local area networks whose operation is based on broadcasting information in source-addressed messages. A source-address is a system wide identifier that reflects unambiguously the place where a message is created. The presented form of communication is particularly well suited for the publication of real-time data in distributed systems. Its advantages over destination-addressed message passing are: no side effects, i.e. messages from different sources cannot interfere with each other at a destination; convenient monitoring of running systems; easy system extension at run time. We discuss broadcast mechanisms for the publication of real-time state and event information and present realized systems for industrial process control.

Broadcasting source-addressed messages (BSM) is introduced as a primary form of communication in distributed computer systems. Each broadcast message is labeled by a source address, which is a unique identifier that reflects the place where the message is created. A node interested in messages of a certain source can filter them from the transmission channel by performing an associative address matching. BSM is an asynchronous communication between the sender and anonymous receivers. We distinguish broadcast strategies with respect to the reliability of transmission - unreliable, reliable - and the type of message receipt - updating, buffering. Advantages of BSM over destination-addressed message passing are: no side effects, convenient monitoring and easy extension of distributed systems at run time. BSM makes possible new forms of distributed computation and is particularly suitable for real-time processing. We present two realized BSM-based systems for distributed control and monitoring of industrial processes.