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- 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.250) Appendix A7.10 Problems solved using the Hamilton-Jacobi Equation

# (p.250) Appendix A7.10 Problems solved using the Hamilton-Jacobi Equation

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

- Publisher:
- Oxford University Press

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- 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