Introduction to Analytical Dynamics

✍ Scribed by Nicholas Woodhouse

• Publisher: Springer
• Year: 2009
• Tongue: English
• Leaves: 248
• Series: Springer Undergraduate Mathematics Series
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xiii
Frames of Reference....Pages 1-33
One Degree of Freedom....Pages 35-66
Lagrangian Mechanics....Pages 67-98
Noether’s Theorem....Pages 99-113
Rigid Bodies....Pages 115-145
Oscillations....Pages 147-160
Hamiltonian Mechanics....Pages 161-182
Geometry of Classical Mechanics....Pages 183-224
Epilogue: Relativity and Quantum Theory....Pages 225-228
Back Matter....Pages 229-240

✦ Subjects

Applications of Mathematics;Mechanics;Theoretical and Applied Mechanics