Description

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 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 illustrate the intellectual beauty/ remarkable power/ and broad scope provided by use of variational principles in physics. This second edition adds discussion of the use of variational principles applied to the following topics: Systems subject to initial boundary conditions The hierarchy of the related formulations based on action/ Lagrangian/ Hamiltonian/ and equations of motion/ to systems that involve symmetries Non-conservative systems. Variable-mass systems. The General Theory of Relativity. The first edition of this book can be downloaded at the publisher link.