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Introduction to Analytical Dynamics

N. M. J. Woodhouse
Publication Date: 
Number of Pages: 
Springer Undergraduate Mathematics Series
[Reviewed by
William J. Satzer
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This is a revised edition of a book first published more than twenty years ago. It is designed to teach analytical mechanics to second and third year undergraduates in the UK, and probably to third or fourth year undergraduates in the US. The preface to the first edition begins, “It may seem odd that Newtonian mechanics should still hold a central place in the university mathematics curriculum”, and then goes on to state the (very good) reasons why that should be so. In the US, mathematics students may see parts of this material as components of courses in dynamical systems or differential equations. But the subject is now firmly established only in physics curricula across the US.

This book offers a very attractive traditional introduction to the subject. All the topics will be familiar to anyone who has taken or taught such a course. The author has two primary goals. The first is to help the student follow the chain of argument that leads from Newton’s formulation of mechanics to Lagrange’s equations, Hamilton’s principle, Hamiltonian equations and canonical transformations. The second is to give practice in problem solving. Many of the examples and exercises are drawn from recent Oxford University exams. Consequently, there are not many routine problems. Prerequisites include some basic linear algebra, the chain rule for partial derivatives and a bit of vector calculus.

The revised edition incorporates one addition and a small reorganization. The new material is a chapter on the geometry of classical mechanics that serves as an introduction to differential geometric methods. The reorganization combines material on systems with one degree of freedom into a separate early chapter. This allows the author to introduce the key ideas of the Lagrangian theory in a familiar setting without having to deal with the complications of multiple indices or the summation convention. Here, as throughout the book, the author is well tuned to the difficulties even strong students encounter.

The author offers a final short section that discusses the relevance of classical mechanics in modern physics, especially to relativity and quantum mechanics.

This is a fine textbook. It would be a pleasure to teach or to learn from it.

Bill Satzer ( is a senior intellectual property scientist at 3M Company, having previously been a lab manager at 3M for composites and electromagnetic materials. His training is in dynamical systems and particularly celestial mechanics; his current interests are broadly in applied mathematics and the teaching of mathematics.

Frames of Reference.- One Degree of Freedom.- Lagrangian Mechanics.- Noether's Theorem.- Rigid Bodies.- Oscillations.- Hamiltonian mechanics.- Geometry of Classical Mechanics.- Epilogue: Relativity and Quantum Theory.- Notes on Exercises.