Variational principles in classical mechanics 1st Edition by Douglas Cline ISBN 0998837253 978-0998837253

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Product details:

ISBN 10: 0998837253 

ISBN 13: 978-0998837253

Author: Douglas Cline

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.

Table of contents:

1 A brief history of classical mechanics
2 Review of Newtonian mechanics 
3 Linear oscillators
4 Nonlinear systems and chaos
5 Calculus of variations
6 Lagrangian dynamics
7 Symmetries, Invariance and the Hamiltonian
8 Hamiltonian mechanics
9 Hamilton’s Action Principle
10 Nonconservative systems
11 Conservative two-body central forces
12 Non-inertial reference frames
13 Rigid-body rotation
14 Coupled linear oscillators
15 Advanced Hamiltonian mechanics
16 Analytical formulations for continuous systems
17 Relativistic mechanics
18 The transition to quantum physics
19 Epilogue

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Tags: Douglas Cline, Variational principles, in classical mechanics