- Title Pages
- Dedication
- Preface
- Acknowledgments
- 1 Basic Dynamics of Point Particles and Collections
- 2 Introduction to Lagrangian Mechanics
- 3 Lagrangian Theory of Constraints
- 4 Introduction To Hamiltonian Mechanics
- 5 The Calculus of Variations
- 6 Hamilton’s Principle
- 7 Linear Operators and Dyadics
- 8 Kinematics of Rotation
- 9 Rotational Dynamics
- 10 Small Vibrations About Equilibrium
- 11 Lagrangian Mechanics with Time as a Coordinate
- 12 Hamiltonian Mechanics with Time as a Coordinate
- 13 Hamilton’s Principle and Noether’s Theorem
- 14 Relativity and Spacetime
- 15 Fourvectors and Operators
- 16 Relativistic Mechanics
- 17 Canonical Transformations
- 18 Generating Functions
- 19 Hamilton–Jacobi Theory
- APPENDIX A VECTOR FUNDAMENTALS
- APPENDIX B MATRICES AND DETERMINANTS
- Appendix C Eigenvalue Problem With General Metric
- Appendix D THE CALCULUS OF MANY VARIABLES
- APPENDIX E GEOMETRY OF PHASE SPACE
- References
- Index

# Hamilton’s Principle and Noether’s Theorem

# Hamilton’s Principle and Noether’s Theorem

- Chapter:
- (p.305) 13 Hamilton’s Principle and Noether’s Theorem
- Source:
- Analytical Mechanics for Relativity and Quantum Mechanics
- Author(s):
### Oliver Johns

- Publisher:
- Oxford University Press

This chapter presents extended forms of Hamilton’s principle and the phase space Hamilton’s principle based on the extended Lagrangian and Hamiltonian methods developed earlier. It also discusses Noether’s theorem, a method for using symmetries of the extended Lagrangian to identify quantities that are conserved during the motion of the system. Noether’s theorem is a powerful technique for discovering conserved quantities in complex Lagrangian systems. The basics of the method are analysed in the simple context of Lagrangian systems with a finite number of degrees of freedom.

*Keywords:*
Noether’s theorem, Hamilton’s principle, phase space, motion, Lagrangian systems, degrees of freedom, conserved quantities

Oxford 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
- Dedication
- Preface
- Acknowledgments
- 1 Basic Dynamics of Point Particles and Collections
- 2 Introduction to Lagrangian Mechanics
- 3 Lagrangian Theory of Constraints
- 4 Introduction To Hamiltonian Mechanics
- 5 The Calculus of Variations
- 6 Hamilton’s Principle
- 7 Linear Operators and Dyadics
- 8 Kinematics of Rotation
- 9 Rotational Dynamics
- 10 Small Vibrations About Equilibrium
- 11 Lagrangian Mechanics with Time as a Coordinate
- 12 Hamiltonian Mechanics with Time as a Coordinate
- 13 Hamilton’s Principle and Noether’s Theorem
- 14 Relativity and Spacetime
- 15 Fourvectors and Operators
- 16 Relativistic Mechanics
- 17 Canonical Transformations
- 18 Generating Functions
- 19 Hamilton–Jacobi Theory
- APPENDIX A VECTOR FUNDAMENTALS
- APPENDIX B MATRICES AND DETERMINANTS
- Appendix C Eigenvalue Problem With General Metric
- Appendix D THE CALCULUS OF MANY VARIABLES
- APPENDIX E GEOMETRY OF PHASE SPACE
- References
- Index