Einfuhrung In Die Physik Bd 3

Dieses Buch beruht auf 40 lahren intensiven Studiums der Differentialglei chungen, sowohl yom theoretischen als auch yom praktischen Gesichtspunkt aus, eines Studiums, das mit meiner Tatigkeit im Rechen-Institut M. Picones in Rom begann, sodann fortgesetzt wurde in der Gruppe flir Industriemathema tik der Luftfahrt-Forschungsanstalt in Braunschweig, und endlich mit meinen Vorlesungen, hauptsachlich an der Universitat Innsbruck, abgeschlossen wurde. Die Zeit der Weltraumfliige stellte hier neue Aufgaben der Bahnberechnung von Satelliten, deren Bearbeitung theoretisch eine geschlossene Formel zur Losung des n-Korper-Problems, praktisch eine neue Methode zur Berechnung von reguJaren Differentialgleichungssystemen zeitigte, die mit den besten bekannten Losungsmethoden erfolgreich in Konkurrenz treten konnte, was vor aHem meinen Mitarbeitern H. Knapp und G. Wanner zu danken war. Die Vorlesung iiber Differentialgleichungen habe ich seit 1947 in regelmaBi gen Abstanden an der Universitat Innsbruck gehalten, bei jeder Wiederholung neu bearbeitet und durch Seminararbeiten vervollstandigt; auch in meiner flir Physik-Studenten besonders gehaltenen Vorlesung iiber {raquo}Die mathemati schen Methoden der Physik{laquo} habe ich in gekiirzter Form immer die {raquo}Differen tialgleichungen{laquo} eingeschlossen. In der vorliegenden Fassung wurde vor allem das zweite Kapitel iiber Diffe rentialgleichungen mit analytischen Koeffizienten, also speziell der hypergeome trischen, Besselschen und Kummerschen Differentialgleichungen' neu gefaBt und einem neuen Ordnungsprinzip, der {raquo}Invariante{laquo}, unterworfen. Damit ge lingt es, jede vorgelegte Differentialgleichung rasch einzuordnen und auf eine dieser Standardformen zu transformieren. Diese Transformationsformeln wur den neu entwickelt und werden hier zum ersten Mal veroffentlicht. Fiir alle Satze und Entwicklungen werden strenge Beweise geboten; z. B.

The first objective of statistical mechanics is to explain the fundamental laws of thermodynamics from first principles based on the atomic structure of matter. This problem was attacked successfully first by MAXWELL and CLAUSIUS in studies on the kinetic theory of gases. It will be treated briefly in Sec. II-A, to gain some understanding and experience before dealing with more general problems. The second objective is then to calculate thermodynamics quantities from the microscopic laws governing the atomic motion. Whenever we try to lay the foundation of thermodynamics on an atomistic theory, we are confronted with a very strange situation. The thermodynamical state of a system is defined uniquely by only a few quantities, such as pressure, volume, energy, temperature, flow velocities, etc. In contrast, the atomistic descrip tion needs an enormous number of variables to define a state, e. g. , positions and velocities of all the atoms involved in classical mechanics or Schrodinger's wave function of the corresponding N body-problem in quantum mechanics. Classical mechanics, for instance, can predict the future development only if all the positions and velocities are known, say at time t = O. The number of values needed for this 23 purpose is of the order of 10 . Actually, only a few parameters are at our disposal from thermodynamics. Therefore, from thermodynamics we know almost nothing about the atomistic situation.

Research and scientific progress are based upqn intuition coordinated with a wide theoretical knowledge, experimental skill, and a realistic sense of the limitations of technology. Only a deep insight into physical phenomena will supply the necessary skills to handle the problems that arise in acoustics. The acoustician today needs to be well acquainted with mathematics, dynamics, hydrodynamics, and physics; he also needs a good knowledge of statistics, signal processing, electrical theory, and of many other specialized subjects. Acquiring this background is a laborious task and would require the study of many different books. It is the goal of this volume to present this background in as thorough and readable a manner as possible so that the reader may turn to specialized publications or chapters of other books for further information without having to start at the preliminaries. In trying to accomplish this goal, mathematics serves only as a tool; the better our understanding of a physical phenomenon, the less mathematics is needed and the shorter and more concise are our computa tions. A word about the choice of subjects for this volume will be helpful to the reader. Even scientists of high standing are frequently not acquainted with the fundamentals needed in the field of acoustics. Chapters I to IX are devoted to these fundamentals. After studying Chapter I, which dis cusses the units and their relationships, the reader should have no difficulty converting from one system of units to any other.

This successful textbook emphasizes the unified nature of all the disciplines of Fluid Mechanics as they emerge from the general principles of continuum mechanics. The different branches of Fluid Mechanics, always originating from simplifying assumptions, are developed according to the basic rule: from the general to the specific. The first part of the book contains a concise but readable introduction into kinematics and the formulation of the laws of mechanics and thermodynamics. The second part consists of the methodical application of these principles to technology. In addition, sections about thin-film flow and flow through porous media are included.

Chiefly translations from foreign aeronautical journals.

These two reports are surveys on the progress and present state of development of dive-control flaps for gliders and airplanes. The second article describes how on the basis of wind tunnel and free-flight tests, the drag increase on brake flaps of the type DFS, can be predicted. Pressure records confirm a two-dimensional load distribution along the brake-flap surface Aerodynamically, the location of the brake flaps along the span is of importance for reasons of avoidance of vibration and oscillation phenomena on control and tail surfaces; statically, because of the magnitude of the frontal drag in diving with respect to the bending moments, which may become decisive for the dimensions of the wing attachment and for the wing covering.