Mathematical Methods of Classical Mechanics (2nd ed.)
| Authors | Arnold, Vladimir Igorevich Vogtmann, K. Weinstein, A. |
| Series | Graduate Texts in Mathematics [60.0] |
| Tags | Mathematics, Global analysis (Mathematics), Analysis, Theoretical Mathematical and Computational Physics |
| Publisher | Springer |
| Published | 17 gen 1989 |
| Date | 21 mar 2017 |
| Languages | eng |
| Identifiers | Amazon.com, uri: https://link.springer.com/book/10.1007/978-1-4757-2063-1, isbn: 9781475720631, oclc: 968649280, doi: 10.1007/978-1-4757-2063-1 |
| Formats | EPUB, PDF |
Description
Arnold is a leading author in the so-called "Russian style" (contra Bourbaki's style).
In this text, the author constructs the mathematical apparatus of classical mechanics from the beginning, examining all the basic problems in dynamics, including the theory of oscillations, the theory of rigid body motion, and the Hamiltonian formalism. This modern approch, based on the theory of the geometry of manifolds, distinguishes iteself from the traditional approach of standard textbooks. Geometrical considerations are emphasized throughout and include phase spaces and flows, vector fields, and Lie groups. The work includes a detailed discussion of qualitative methods of the theory of dynamical systems and of asymptotic methods like perturbation techniques, averaging, and adiabatic invariance.