Introduction to Analytical Dynamics

This is a revised edition of a text on classical mechanics published twenty years ago. The presentation has been simplified, and feedback has been incorporated into the text, thus greatly improving the content and style, making it fresher and more compelling.

First published in 1987, this text offers concise but clear explanations and derivations to give readers a confident grasp of the chain of argument that leads from Newton's laws through Lagrange's equations and Hamilton's principle, to Hamilton's equations and canonical transformations. This new edition has been extensively revised and updated to include: A chapter on symplectic geometry and the geometric interpretation of some of the coordinate calculations. A more systematic treatment of the conections with the phase-plane analysis of ODEs; and an improved treatment of Euler angles. A greater emphasis on the links to special relativity and quantum theory showing how ideas from this classical subject link into contemporary areas of mathematics and theoretical physics. A wealth of examples show the subject in action and a range of exercises with solutions are provided to help test understanding.

A new edition of a classic text, extensively revised and updated in order to simplify the presentation and offer a more modern outlook, showing how ideas from classical mechanics link with contemporary research. Aims to give readers a confident grasp of the material by confronting, rather than evading, common notational and pedagogical difficulties encountered on the journey from Newton to Lagrange and Hamilton.

Klappentext

Analytical dynamics forms an important part of any undergraduate programme in applied mathematics and physics: it develops intuition about three-dimensional space and provides invaluable practice in problem solving.

First published in 1987, this text is an introduction to the core ideas. It offers concise but clear explanations and derivations to give readers a confident grasp of the chain of argument that leads from Newton's laws through Lagrange's equations and Hamilton's principle, to Hamilton's equations and canonical transformations.

This new edition has been extensively revised and updated to include:

• A chapter on symplectic geometry and the geometric interpretation of some of the coordinate calculations.

• A more systematic treatment of the conections with the phase-plane analysis of ODEs; and an improved treatment of Euler angles.

• A greater emphasis on the links to special relativity and quantum theory, e.g., linking Schrödinger's equation to Hamilton-Jacobi theory, showing how ideas from this classical subject link into contemporary areas of mathematics and theoretical physics. Aimed at second- and third-year undergraduates, the book assumes some familiarity with elementary linear algebra, the chain rule for partial derivatives, and vector mechanics in three dimensions, although the latter is not essential. A wealth of examples show the subject in action and a range of exercises - with solutions - are provided to help test understanding.

Inhalt
Frames of Reference.- One Degree of Freedom.- Lagrangian Mechanics.- Noether#x2019;s Theorem.- Rigid Bodies.- Oscillations.- Hamiltonian Mechanics.- Geometry of Classical Mechanics.- Epilogue: Relativity and Quantum Theory.