Вариационное исчисление и классическая механика: аналитические методы для частиц и колебаний

This text provides the mathematical foundation for calculus of variations to be applied to classical mechanics. Proofs of the major theorems and principles of classical mechanics are provided. The book includes many details which are missing from most standard texts. Topics include: formulations of Lagrangian and Hamiltonian dynamics, linear and nonlinear oscillations, discontinuous potentials, inclined plane problems, central force motion, 2-body collisions, and an introduction to kinetic theory. The author holds the controversial view that simple problems are not always simple. Some “simple” problems require careful examination. These problems are often used as models to explain more complex phenomena. It is assumed that the reader has a solid background in differential equations, advanced calculus, and intermediate mechanics. The book is intended for advanced undergraduate or beginning graduate students in physics or applied mathematics.