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Classical mechanics. 3rd completely revised and expanded ed. (Klassische Mechanik.) (German) Zbl 1132.70001

Lehrbuch Physik. Berlin: Wiley-VCH (ISBN 978-3-527-40589-3). xiv, 686 p. (2006).
[For reviews of the previous editions see Zbl 0043.18001, Zbl 0315.70001 and Zbl 0491.70001.]
During about sixty years since the first edition (by the first author) of this work did appear, it became a well-known standard textbok on mechanics of particles and systems, intended especially for physicists. A revised and expanded edition appeared thirty years ago. The actual edition has been rewritten by the last two authors bringing new informations, completing the applications and maintaining its high scientific level. The book tries to explain the best possible the physical phenomena, not exceeding a student level concerning the necessary mathematical knowledge. Many modern aspects, especially those involving physics (quantum mechanics, elementary particle physics, special theory of relativity, classical chaos etc.) have to be emphasized. As well, the introduction of the perturbation theory as a numerical method of analysis is noteworthy. Any chapter ends with applications and exercises, leading to deepen both the physical knowledge and the mathematical tools introduced, e.g. properties of groups (which allows the statement of Noether’s theorem), tensors in non-Euclidean spaces etc.
We mention the contents of the book: 1. Fundamental principles; 2. Variational principles and Lagrange’s equations; 3. Central forces; 4. Kinematics of rigid solids; 5. Equations of motion of rigid solids; 6. Vibrations; 7. Classical mechanics of special theory of relativity; 8. Hamilton’s equations of motion; 9. Canonical transformations; 10. The Hamilton-Jacobi theory and action-angle variables; 11. Classical chaos; 12. Canonical perturbation theory; 13. Hamiltonian and Lagrangian formulations for continuous systems and fields. We mention also two mathematical appendices and a reach bibliography for each chapter.
This volume represents an excellent contributions to university textbooks and can he recommended to both students and teachers who wish to clear up their knowledge in the field.

MSC:

70-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mechanics of particles and systems
70Hxx Hamiltonian and Lagrangian mechanics
70Fxx Dynamics of a system of particles, including celestial mechanics
70Exx Dynamics of a rigid body and of multibody systems
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