The Principle of Least Action underlies all physics and leads into quantum mechanics and Einstein's Relativity. There are some textbooks that do the calculations, and one book with nice pictures, but no book (before this one) that explains what 'action' is, and why nature follows this principle.
The Principle of Least Action underlies all physics and leads into quantum mechanics and Einstein's Relativity. There are some textbooks that do the calculations, and one book with nice pictures, but no book (before this one) that explains what 'action' is, and why nature follows this principle.
Jennifer Coopersmith took her PhD in nuclear physics from the University of London, and was later a research fellow at TRIUMF, University of British Columbia. She was for many years an associate lecturer for the Open University (London and Oxford), and was then a tutor on astrophysics courses at Swinburne University of Technology in Melbourne while based at La Trobe University in Bendigo, Victoria. She now lives in France.
Inhaltsangabe
1: Introduction 2: Antecedents 3: Mathematics and physics preliminaries 4: The Principle of Virtual Work 5: D'Alembert's Principle 6: Lagrangian Mechanics 7: Hamiltonian Mechanics 8: The whole of physics 9: Final words Appendices A1.1: Newton's Laws of Motion A3.1: Reversible Displacements A2.1: Portraits of the physicists A6.1: Worked examples in Lagrangian Mechanics A6.2: Proof that T is a function of v² A6.3: Energy conservation and the homogeneity of time A6.4: The method of Lagrange Multipliers A6.5: Generalized Forces A7.1: Hamilton's Transformation, Examples A7.2: Demonstration that the p¿s are independent coordinates A7.3: Worked examples in Hamiltonian Mechanics A7.4: Incompressibility of the phase fluid A7.5: Energy conservation in extended phase space A7.6: Link between the action, S, and the 'circulation' A7.7: Transformation equations linking p and q via S A7.8: Infinitesimal canonical transformations A7.9: Perpendicularity of wavefronts and rays A7.10: Problems solved using the Hamilton-Jacobi Equation A7.11: Quasi refractive index in mechanics A7.12: Einstein's link between Action and the de Broglie waves
1: Introduction 2: Antecedents 3: Mathematics and physics preliminaries 4: The Principle of Virtual Work 5: D'Alembert's Principle 6: Lagrangian Mechanics 7: Hamiltonian Mechanics 8: The whole of physics 9: Final words Appendices A1.1: Newton's Laws of Motion A3.1: Reversible Displacements A2.1: Portraits of the physicists A6.1: Worked examples in Lagrangian Mechanics A6.2: Proof that T is a function of v² A6.3: Energy conservation and the homogeneity of time A6.4: The method of Lagrange Multipliers A6.5: Generalized Forces A7.1: Hamilton's Transformation, Examples A7.2: Demonstration that the p¿s are independent coordinates A7.3: Worked examples in Hamiltonian Mechanics A7.4: Incompressibility of the phase fluid A7.5: Energy conservation in extended phase space A7.6: Link between the action, S, and the 'circulation' A7.7: Transformation equations linking p and q via S A7.8: Infinitesimal canonical transformations A7.9: Perpendicularity of wavefronts and rays A7.10: Problems solved using the Hamilton-Jacobi Equation A7.11: Quasi refractive index in mechanics A7.12: Einstein's link between Action and the de Broglie waves
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