000			03259nam a2200385 4500
001			OTLid0000490
003			MnU
005			20201105133334.0
006			m o d s
008			180907s2018 mnu o 0 0 eng d
020			_a9780998837260
040			_aMnU _beng _cMnU
050		4	_aQH301
050		4	_aQC21.3
100	1		_aCline, Douglas _eauthor
245	0	0	_aVariational Principles in Classical Mechanics _cDouglas Cline
250			_aSecond Edition
264		2	_bOpen Textbook Library
264		1	_bUniversity of Rochester River Campus Libraries
300			_a1 online resource
490	0		_aOpen textbook library.
505	0		_aContents -- Preface -- Prologue -- 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 Conservative two-body central forces -- 10 Non-inertial reference frames -- 11 Rigid-body rotation -- 12 Coupled linear oscillators -- 13 Hamilton's principle of least action -- 14 Advanced Hamiltonian mechanics -- 15 Analytical formulations for continuous systems -- 16 Relativistic mechanics -- 17 The transition to quantum physics -- 18 Epilogue -- Appendices
520	0		_aTwo 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.
542	1		_fAttribution-NonCommercial-ShareAlike
546			_aIn English.
588	0		_aDescription based on print resource
650		0	_aScience _vTextbooks
650		0	_aPhysics _vTextbooks
710	2		_aOpen Textbook Library _edistributor
856	4	0	_uhttps://open.umn.edu/opentextbooks/textbooks/490 _zAccess online version
999			_c19873 _d19873