Patrick Hamill

A concise but rigorous treatment of variational techniques, focussing primarily on Lagrangian and Hamiltonian systems, this book is ideal for physics, engineering, and mathematics students. A Student’s Guide to Lagrangians and Hamiltonians begins by applying Lagrange’s equations to several mechanical systems.

It introduces the concepts of generalized coordinates and generalized momentum. Following this, the book turns to the calculus of variations to derive the Euler–Lagrange equations. It introduces Hamilton’s principle and uses this throughout the book to derive different results.

The Hamiltonian, Hamilton’s equations, canonical transformations, Poisson brackets, and Hamilton–Jacobi theory are considered next. The book concludes by discussing continuous Lagrangians and Hamiltonians and how they relate to field theory. Written in clear, simple language and featuring numerous worked examples and exercises to help students master the material, this book is a valuable supplement to courses in mechanics.