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Many different mathematical methods and concepts are used in classical mechanics: differential equations and phase flows, 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 theoret.ical mechanics as taught by mathematicians. A considerable part of the book is devoted to variational principles and analytical dynamics.
Arguably, the applicability of a mathematical theory (or its links with other well established parts of this science) is what makes it important. This book serves to justify in this sense the study of ordinary differential equations, calculus of variations, Riemannian geometry, symplectic geometry, Lie groups and Lie algebras, manifold theory as well as other more specialized subjects such as integrable systems or catastrophe theory.
Best Sellers Rank: #41 in Physics of Mechanics
#60 in Mathematical Physics
#69 in Mathematical Analysis