Show Summary Details

- Title Pages
- Frontispiece
- Dedication
- Epigraph
- Preface
- List of Figures
- 1 Introduction
- 2 Antecedents
- 3 Mathematics and physics preliminaries: of hills and plains and other things
- 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
- Appendix A1.1 Newton’s Laws of Motion
- Appendix A2.1 Portraits of the physicists
- Appendix A3.1 Reversible displacements
- Appendix A6.1 Worked examples in Lagrangian Mechanics
- Appendix A6.2 Proof that T is a function of v2
- Appendix A6.3 Energy conservation and the homogeneity of time
- Appendix A6.4 The method of Lagrange Multipliers
- Appendix A6.5 Generalized Forces
- Appendix A7.1 Hamilton’s Transformation, examples
- Appendix A7.2 Demonstration that the pi s are independent coordinates
- Appendix A7.3 Worked examples in Hamiltonian Mechanics
- Appendix A7.4 Incompressibility of the phase fluid
- Appendix A7.5 Energy conservation in extended phase space
- Appendix A7.6 Link between the action, S, and the ‘circulation’
- Appendix A7.7 Transformation equations linking p and q via S
- Appendix A7.8 Infinitesimal canonical transformations
- Appendix A7.9 Perpendicularity of wavefronts and rays
- Appendix A7.10 Problems solved using the Hamilton-Jacobi Equation
- Appendix A7.11 Quasi refractive index in mechanics
- Appendix A7.12 Einstein’s link between Action and the de Broglie waves
- Bibliography and Further Reading
- Index

# (p.244) Appendix A7.8 Infinitesimal canonical transformations

# (p.244) Appendix A7.8 Infinitesimal canonical transformations

- Source:
- The Lazy Universe
- Author(s):
### Jennifer Coopersmith

- Publisher:
- Oxford University Press

British Academy Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us.

- Title Pages
- Frontispiece
- Dedication
- Epigraph
- Preface
- List of Figures
- 1 Introduction
- 2 Antecedents
- 3 Mathematics and physics preliminaries: of hills and plains and other things
- 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
- Appendix A1.1 Newton’s Laws of Motion
- Appendix A2.1 Portraits of the physicists
- Appendix A3.1 Reversible displacements
- Appendix A6.1 Worked examples in Lagrangian Mechanics
- Appendix A6.2 Proof that T is a function of v2
- Appendix A6.3 Energy conservation and the homogeneity of time
- Appendix A6.4 The method of Lagrange Multipliers
- Appendix A6.5 Generalized Forces
- Appendix A7.1 Hamilton’s Transformation, examples
- Appendix A7.2 Demonstration that the pi s are independent coordinates
- Appendix A7.3 Worked examples in Hamiltonian Mechanics
- Appendix A7.4 Incompressibility of the phase fluid
- Appendix A7.5 Energy conservation in extended phase space
- Appendix A7.6 Link between the action, S, and the ‘circulation’
- Appendix A7.7 Transformation equations linking p and q via S
- Appendix A7.8 Infinitesimal canonical transformations
- Appendix A7.9 Perpendicularity of wavefronts and rays
- Appendix A7.10 Problems solved using the Hamilton-Jacobi Equation
- Appendix A7.11 Quasi refractive index in mechanics
- Appendix A7.12 Einstein’s link between Action and the de Broglie waves
- Bibliography and Further Reading
- Index