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Book review

Author(s) Schneider, Manfred
Title Himmelsmechanik, Band I, 3rd edition
Publisher Wissenschaftsverlag
Year of publication 1992
Reviewed by Cristina Blaga

The book under review is the first volume of a series of three volumes devoted to celestial mechanics. The author, a renown expert in the field, approaches the subject from a modern point of view. This volume is concerned with the fundamentals of celestial mechanics and with the problem of the determination of motion from the initial data or from a boundary value problem in the framework of classical (Newtonian) mechanics.

The first part of the book includes the structure of the Newtonian spacetime and then, having in mind that in celestial mechanics we are dealing with systems of corps (pointlike or continuous media), there are discussed in some details the equations of balance for systems of pointlike particles and for continuous media. This part ends with the canonical formalism and the Hamilton-Jacobi theory. The second part has as a main goal, the determination of the orbit from the initial data or from the conditions on the boundary. The next step is the study of the long time behavior of nonlinear dynamical systems (i.e. the interpretation of celestial mechanics from a dynamical systems point of view).

The book, in excellent graphical conditions, with a lot of pictures and tables illustrating and systemizing the developed theory, is intended for the students in astronomy, physics or geodesy and for the researchers from the fields mentioned above.

Those which are not familiar with the mathematical formalism used within the book can start the reading with the two appendices (one of them is dealing with the solution of the systems of linear algebra to equations by Gauss method while the second is devoted to the selfadjoint boundary value problem for second order differential operators).

At the end of the book there are an index and a list of notation, helping the reader in the using of the book. There is, also, an extended list of references. In my opinion, if someone is decided to learn celestial mechanics in its modern formulation, this is the book to use. Unfortunately, the language in which it is written will restrict the range of readers. It would be very good if the author will decide to publish, also, an English version.