Introduction to mechanics and symmetry. A basic exposition of classical mechanical systems. 2nd ed. (English) Zbl 0933.70003

Marsden, Jerrold E.; Ratiu, Tudor S.

Texts in Applied Mathematics. 17. New York, NY: Springer. xviii, 582 p. (1999).

[See the review of the first edition (1994; Zbl 0811.70002).]
In the second edition, the main structural changes are the creation of a solution manual (along with many more exercises in the text) and the Internet supplements (both free available on the Internet, see http://www.cds.caltech.edu/~marsden/books/node18.html) The Internet supplements contain, for example, the material on the Maslov index that was not needed for the main flow of the book. As for the text, some parts of the book were rewritten to improve the flow of material and to correct inaccuracies. Some examples: The material on the Hamilton-Jacobi theory was completely rewritten, a new section on Routh reduction (§8.9) was added, Chapter 9 on Lie groups was substantially improved and expanded. The presentation of examples of coadjoint orbits (Chapter 14) was improved by stressing matrix methods throughout.

MSC:

70-02	Research exposition (monographs, survey articles) pertaining to mechanics of particles and systems
70Hxx	Hamiltonian and Lagrangian mechanics
37N05	Dynamical systems in classical and celestial mechanics
57R25	Vector fields, frame fields in differential topology

Keywords:

stability; bifurcation; rigid body; heavy top; Maxwell-Vlasov system; Poisson-Vlasov brackets; momentum mappings; Lie group actions; geometric phase; Marsden-Weinstein reduction theory; incompressible fluids; chaos; resonances; solution manual; Internet supplements; Maslov index; Hamilton-Jacobi theory; Routh reduction; coadjoint orbits; matrix methods