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Bestseller
BestsellerE-book
Author Cline, Douglas, author.

Title Variational principles in classical mechanics / Douglas Cline, University of Rochester ; illustrator, Meghan Sarkis.

Publication Info. Rochester, NY : University of Rochester River Campus Libraries, University of Rochester, [2017]-
Minneapolis : Open Textbook Library
©2017-

Item Status

Description 1 online resource : illustrations (some colour).
Current Frequency Updated irregularly.
Physical Medium polychrome
Description text file
Series Open textbook library
Open Textbook Library.
Bibliography Includes bibliographical references and index.
Contents A brief history of classical mechanics -- Review of Newtonian mechanics -- Linear oscillators -- Nonlinear systems and chaos -- Calculus of variations -- Lagrangian dynamics -- Symmetries, invariance and the Hamiltonian -- Hamiltonian mechanics -- Conservative two-body central forces -- Non-inertial reference frames -- Rigid-body rotation -- Coupled linear oscillators -- Hamilton's principle of least action -- Advanced Hamiltonian mechanics -- Analytical formulations for continuous systems -- Relativistic mechanics -- The transition to quantum physics -- Appendices: Matrix algebra ; Vector algebra ; Orthogonal coordinate systems ; Coordinate transformations ; Tensor algebra ; Aspects of multivariate calculus ; Vector differential calculus ; Vector integral calculus ; Waveform analysis.
Summary "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."--Open Textbook Library.
System Details Mode of access: World Wide Web.
Note Variational Principles in Classical Mechanics by Douglas Cline is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License (CC BY-NC-SA 4.0), except where otherwise noted.
Local Note Open Educational Resources (OER). Open Textbooks
Open Textbook Library
Subject Mechanics.
Mechanics.
Variational principles.
Variational principles.
Quantum theory.
Quantum theory.
Genre/Form Textbooks.
Textbooks.
Added Author Sarkis, Meghan, illustrator.
Open Textbook Library, distributor.
ISBN 9780998837246 (e-book (Adobe PDF color)
0998837245 (e-book (Adobe PDF color)
9780998837260
0998837261
9780998837253 (print (paperback grayscale)
0998837253 (print (paperback grayscale)