Mechanics

Mechanics - Stefan Banach

My lectures in mechanics, given for many years at the Jan Kazimierz University and the Lwów Polytechnic Institute, consisted of the contents of this work. I have limited myself to the mechanics of a system of material points and a rigid body. The material covered is suitable in general for university requirements, however, keeping in mind the needs of the students at the Polytechnic Institute, chapter VI which treats of the statics of a rigid body was worked out so that it could be accessible without a knowledge of kinematics and dynamics. It can be read immediately after chapter I when supplemented with several facts according to instructions included in the footnote on p. 231. Taking into account the requirements in mechanics at the Polytechnic Institute, I have also given in chapter VI certain information from engineering mechanics. The mathematics necessary to understand this work in its entirely is limited to the elements of analytic geometry as well as to the differential and integral calculus. Other necessary notions and theorems have been given in the text in order not to send the reader to works too specialized. In particular, I give in the Appendix (at the end of the work) a method of solving ordinary differential equations of second order with constant coefficients which arise frequently in mechanics. I have endeavoured to give in this book as easy an exposition as possible. The more difficult considerations are illustrated by many examples. Problems to be solved have not been inserted in the text; the reader will find them in most textbooks and in the collections of problems which are given below. I have also considered it unnecessary to burden the contents with the names of the authors of particular theorems or examples, since I consider the material contained in this book as classical. The reader will find detailed bibliographic instructions in corresponding articles of volume IV of the Enzyklopädie der mathematischen Wissenschaften (Teubner, Leipzig 1901-1935) as well as in volume V of the work Handbuch der Physik (Berlin 1927), and historical data and critical remarks in the work of E. Mach Die Mechanik in ihrer Entwicklung (9 Aufl., Leipzig 1933). Here I limit myself to the presentation from literature of a number of the more important works, namely: (...) It is a pleasure for me to thank Dr Bronisław Knaster for his effective help in connection with the publishing of this book, Dr Edward Otto for making the drawings and Dr Antoni Zygmund for help in the corrections. Stefan Banach. Lwów, January, 1938.