Introduction to analytical dynamics / N. M. J. Woodhouse

Analytical dynamics forms an important part of any undergraduate program in applied mathematics and physics. The main intention of the book is, first, to give a confident understanding of arguments that lead from Newton’s laws through Lagrange’s equations and Hamilton’s principle to Hamilton’s equations and canonical transformations, and, secondly, to give practice in solving problems.

The book consists of nine chapters. The author defines the basic concepts of kinematics in the first chapter. The main principles of analytical mechanics in the elementary case of body motion with one degree of freedom are considered in the second chapter. The third chapter is devoted to derivation and analysis of Lagrange’s equations for holonomic system with several degrees of freedom. In the fourth chapter Noether’s theorem is stated and its connection with mechanics conservation laws is analysed. The foundations of the dynamics of a rigid body are given in the fifth chapter, illustrated by the body motion with nonholonomic constraints. The sixth chapter is devoted to oscillations of systems with several degrees of freedom in a vicinity of the equilibrium position. In the seventh chapter, the author presents the basic concepts of Hamiltonian mechanics, including the Hamilton-Jacobi equations, Poisson brackets and the theory of canonical transformations. Interconnections of analytical mechanics with geometry and topology are considered in the eighth chapter, whereas the last chapter describes applications of analytical mechanics in quantum mechanics and relativity theory.

The book is aimed at second- and third-year undergraduates. A wealth of examples show analytical mechanics in action, and some exercises with solutions are provided to help the reader’s understanding. (Zentralblatt)