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Book review

Author(s) Scheck, F.
Title Mechanics, From Newton's laws to deterministic chaos
Publisher Springer
Year of publication 1990
Reviewed by Heinz Ulbricht

Mechanics - basis for all of theoretical physics - got an interesting development in the last years. So it is very useful to extend the classical representation of this field by an modern integrativ description. This is one aim of the English version of Scheck's book which was translated from the 2nd German edition. The book integrates the various aspects of classical mechanics, relativistic mechanics and topics such as nonlinearities, instabilities and deterministic chaos.

With the Newtonian mechanics as a starting point elementary dynamics of one-, two-, and many-body systems for unconstrained systems are developed in chapter 1.

Principles of canonical mechanics in Hamiltonian and Lagrangian formulations and the mechanics of rigid bodies are outlined in the following two chapters. Particular attention is dedicated the theory of spinning tops. Chapter 4 deals with relativistic kinematics and dynamics and develops the elements of special relativity. In chapter 5 the intimate connection is shown between mechanics and differential geometry. This chapter may help to bridge the gap between physics of mechanics and the modern mathematical literature on this subject. The 6th chapter provider a concentrated introduction to the fascinating theory of stability and deterministic chaos. All important concepts and special applications of this field are given. A short introduction to continuous systems concludes the book. Exercises and practical examples complete the volume.

An adequate bibliography and an extensive subject index is available.

The book has an modern mathematical level and emphasizes the algebraic description. It is well produced and may be recommended to students, graduates, teachers and mature scientists in related areas.