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Mathematical Methods of Classical Mechanics
Introduction
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.
Keywords
Lagrangian mechanics Mathematische Physik Mechanik Rigid body Vector field classical mechanics differential equation
Authors and affiliations
- 1.Department of Mathematics Steklov Mathematical InstituteRussian Academy of SciencesMoscowRussia
Bibliographic information
- DOIhttps://doi.org/10.1007/978-1-4757-2063-1
- Copyright InformationSpringer-Verlag New York 1989
- Publisher NameSpringer, New York, NY
- eBook PackagesSpringer Book Archive
- Print ISBN978-1-4419-3087-3
- Online ISBN978-1-4757-2063-1
- Series Print ISSN0072-5285
- Buy this book on publisher's site
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