- Title Pages
- Dedication
- Preface
- Acknowledgements
- List of Figures
- 1 The variational principle
- 2 Conservation laws
- 3 The simple pendulum
- 4 The Kepler problem
- 5 The rigid body
- 6 Geometric theory of ordinary differential equations
- 7 Hamilton’s principle
- 8 Geodesics
- 9 Hamilton–Jacobi theory
- 10 Integrable systems
- 11 The three body problem
- 12 The restricted three body problem
- 13 Magnetic fields
- 14 Poisson and symplectic manifolds
- 15 Discrete time
- 16 Dynamics in one real variable
- 17 Dynamics on the complex plane
- 18 KAM theory
- Further reading
- Index
Conservation laws
Conservation laws
- Chapter:
- (p.7) 2 Conservation laws
- Source:
- Advanced Mechanics
- Author(s):
S. G. Rajeev
- Publisher:
- Oxford University Press
Every variable (function) on the phase space has a conjugate variable. If the action is independent of a variable, then its conjugate is a conserved quantity. Energy (Hamiltonian) is shown to be conserved. A digression applies this method to solve the problem for a minimal surface of revolution (catenary).
Keywords: conservation laws, Hamiltonian, conjugate variable, catenary, phase space
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- Title Pages
- Dedication
- Preface
- Acknowledgements
- List of Figures
- 1 The variational principle
- 2 Conservation laws
- 3 The simple pendulum
- 4 The Kepler problem
- 5 The rigid body
- 6 Geometric theory of ordinary differential equations
- 7 Hamilton’s principle
- 8 Geodesics
- 9 Hamilton–Jacobi theory
- 10 Integrable systems
- 11 The three body problem
- 12 The restricted three body problem
- 13 Magnetic fields
- 14 Poisson and symplectic manifolds
- 15 Discrete time
- 16 Dynamics in one real variable
- 17 Dynamics on the complex plane
- 18 KAM theory
- Further reading
- Index
