Two dramatically different philosophical approaches to classical mechanics were developed 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 powerful variational formulations have become the preeminent philosophical approach used in modern science, as well as having applications to other fields such as economics and engineering.
This book introduces variational principles, and illustrates the intellectual beauty, the remarkable power, and the broad scope, of applying variational principles to classical mechanics. A brief review of Newtonian mechanics compares and contrasts the relative merits of the intuitive Newtonian vectorial formulation, with the more powerful analytical variational formulations. Applications presented cover a wide variety of topics, as well as extensions to accommodate relativistic mechanics, and quantum theory.
Neal P. McCluskey ed. and Jason Bedrick ed
Though his life was cut tragically short in 2016, Andrew Coulson had a remarkable impact on education policy. As director of the Cato Institute’s Center for Educational Freedom from 2005 to 2015, he consistently advocated for free-market reforms that would make schools more flexible, innovative, and responsive to parents and students. In this newly published volume, prominent education thinkers who knew Andrew well commemorate his legacy with explorations, expansions, and critiques of his ideas.