ENGLISH

Mathematical Methods of Classical Mechanics

By V. I. Arnold

Book information

Publisher
Springer
Year
2013
ISBN
1475716931, 9781475716931
Google Books ID
UOQlBQAAQBAJ
Language
english
Format
EPUB
Filesize
9 MB (9867969 bytes)
Series
Graduate Texts in Mathematics 60
Pages
464\0
Topic
Physics Mechanics
Time added
2017-03-03 12:40:44

Description

Many different mathematical methods and concepts are used in classical mechanics: differential equations and phase ftows, smooth mappings and manifolds, Lie groups and Lie algebras, symplectic geometry and ergodic theory. Many modern mathematical theories arose from problems in mechanics and only later acquired that axiomatic-abstract form which makes them so hard to study. In this book we construct the mathematical apparatus of classical mechanics from the very beginning; thus, the reader is not assumed to have any previous knowledge beyond standard courses in analysis (differential and integral calculus, differential equations), geometry (vector spaces, vectors) and linear algebra (linear operators, quadratic forms). With the help of this apparatus, we examine all the basic problems in dynamics, including the theory of oscillations, the theory of rigid body motion, and the hamiltonian formalism. The author has tried to show the geometric, qualitative aspect of phenomena. In this respect the book is closer to courses in theoretical mechanics for theoretical physicists than to traditional courses in theoretical mechanics as taught by mathematicians.

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