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Variational Principles in Classical Mechanics Douglas Cline

By: Contributor(s): Material type: TextTextSeries: Open textbook libraryDistributor: Minneapolis, MN Open Textbook LibraryPublisher: Monroe County, New York University of Rochester River Campus Libraries 2019Copyright date: ©2018Edition: Revised Second EditionDescription: 1 online resourceContent type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9780998837260
Subject(s): LOC classification:
  • QH301
  • QC21.3
Online resources:
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
Subject: 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.
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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

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.

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