Two dramatically different philosophical approaches to classical mechanics were proposed during the 17th-18th centuries. Newton developed his vectorial formulation that uses time-dependent differential equations of motion to relate vector observables like force and rate of change of momentum. Euler, Lagrange, Hamilton, and Jacobi, developed powerful alternative variational formulations based on the assumption that nature follows the principle of least action. These variational formulations now play a pivotal role in science and engineering.

This book introduces the variational principles, and their application to classical mechanics. The relative merits of the intuitive Newtonian vectorial formulation, and the more powerful variational formulations, are compared. Applications to a wide variety of topics are used to illustrate the intellectual beauty, remarkable power, and broad scope provided by use of variational principles in physics.

This third edition is closely coupled to the new, interactive, on-line, LibreTexts version of this book. This book emphasizes the important role played by the Poisson Bracket formulation of Hamiltonian mechanics in science and engineering.

Douglas Cline is a Professor of Physics in the Department of Physics and Astronomy, University of Rochester, Rochester, N.Y. He can be contacted through his website.

The first edition of this book can be downloaded here. The second (non-revised) edition of this book can be downloaded here. The revised second edition of this book can be downloaded gateio. Archival copies of all editions can be found here.