Geometric mechanics
A study seminar series, fall of 2011.
Schedule
We will try to meet once a week, either on Wednesday 14:15–15:00 or on Friday 13:15–14:00, depending on if there are other DNA seminars in the same time slots.
| Date | Time | Speaker | Topic |
|---|---|---|---|
| 04.11 | 13:15–14:00 | Brynjulf | Momentum maps |
| 26.10 | 13:15–14:00 | Johannes | From classical to quantum mechanics |
| 07.10 | 13:15–14:00 | Olivier | Mechanical systems with constraints |
| 05.10 | 14:15–15:00 | Geir | Generating functions |
| 16.09 | 13:30–14:15 | Håkon | The connection between Lagrangian and Hamiltonian mechanics |
| 07.09 | 14:15–15:00 | Olivier | Symplectic and Poisson formulation of mechanics |
| 02.09 | 13:15–14:00 | Olivier | Newtonian, Lagrangian and Hamiltonian formulation of mechanics |
Suggested topics
A is Arnold's book (Mathematical Methods of Classical Mechanics 2nd edition), and M is Marsden and Ratiu's book (Introduction to Mechanics and Symmetry 2nd edition).
- General presentation of mechanics: Newton's law, Variational Principle, Symplectic structure and Poisson systems.
- (Simple introduction to differential geometry (manifolds, vector fields, Lie groups and Lie algebras, tangent maps, tangent and cotangent bundles, Lie group actions and their lifts, differential forms, symplecticity) (M §4, §9))
- Interaction between Lagrangian and Hamiltonian formulation (canonical one-form, Legendre transformation) (M start of §7)
- Euler–Poincaré/Lie–Poisson reduction (M §13)
- Momentum map (A §A5, M §11, §12)
- Completely integrable systems? KAM? (A §A8, see also Goldstein's book (Classical Mechanics 3rd edition) §11.2)
- Noether's theorem? (symmetry, conservations laws) (A §20, M §11.4)
- Hamilton–Jacobi equation? (canonical transformations, generating functions) (A §47, §48, M §6.5, §7.9)
If you have some other topic you would like to talk about or discuss, you are more than welcome to do so.
Some style advice
- Show simple examples
- Avoid formalism as much as possible
- Aim for clarity, not generality