عنوان

Variational principles in classical mechanics /

0998837245

0998837261

9780998837246

9780998837260

0998837253

9780998837253

Variational principles in classical mechanics /

[Book]

Douglas Cline, University of Rochester ; illustrator, Meghan Sarkis.

Rochester, NY :

Minneapolis :

University of Rochester River Campus Libraries, University of Rochester,

Open Textbook Library

[2017]-

©2017-

1 online resource :

illustrations (some colour)

Open textbook library

Includes bibliographical references and index.

Updated irregularly.

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.

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"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.

Mode of access: World Wide Web.

Mechanics.

Quantum theory.

Variational principles.

Mechanics.

Quantum theory.

Variational principles.

Cline, Douglas

Sarkis, Meghan

Open Textbook Library,distributor.

20200822145213.0

[Book]

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