J.M. Souriau Structure of Dynamical Systems

Annotation

It is with great pleasure that we are able to provide the reader with a translation of Souriau's elassical text "Structure des Systemes Dy- namiques" on mechanics. We have added the subtitle "a symplectic view of physics", which is elose to the title first proposed by the author. Compared to the French version, we have made several changes in nota- tion for the English edition, all of which have the author's approval. The most important change is that the symbol V' for the exterior derivative of differential forms has been replaced by the symbol d. Consequently in order to avoid confusion, the symbols d, d', ... for vector fields have been replaced by 8, 8', .... We warn the reader that differential forms are always given in terms of their action on tangent vectors and not in 2 terms of a dual basis. We use this opportunity to thank C. Sacn of the University of Lille I for doing all the computer graphics.