Seminar (Completely Integrable Systems II) (Winter Semester 2021/22)
- Lecturer: JProf. Dr. Xian Liao
- Classes: Seminar (0123550)
- Weekly hours: 2
This seminar is a continuation of the seminar ( Completely Integrable System I) held online in SS2021 at KIT. We propose to continue with Arnold’s well-known book 1 on the mathematical methods on classical mechanics.
If you are interested in participating in this seminar, please write an email, with possibly interested topics and with the preferred starting date of the seminar, to xian.liao@kit.edu as soon as possible.
This seminar is expected to take place at earliest in November 2021.
| Schedule | ||
|---|---|---|
| Seminar: | Friday 14:00-15:30 | 20.30 -1.009 |
| Lecturers | ||
|---|---|---|
| Lecturer | JProf. Dr. Xian Liao | |
| Office hours: Monday, 12:00 - 13:00. | ||
| Room 3.027 Kollegiengebäude Mathematik (20.30) | ||
| Email: xian.liao@kit.edu | ||
We will begin with a review talk on the materials covered in SS2021
0. Newtonian mechanics and Lagrangian mechanics (Sections 1-21 1)
and propose the following topics:
1. Linearization and small oscillations. (Sections 22-23 1)
2. Characteristic frequencies and parametric resonance. (Sections 24-25 1)
3. Inertial forces and Coriolis force. (Sections 26-27 1)
4. Rigid bodies. (Sections 28-29 1)
5. Lagrange’s top. (Sections 30-31 1)
6. Exterior forms and differential forms. (Sections 32-34 1)
7. Exterior differentiation. (Sections 35-36 1)
8. Symplectic structure and Lie algebra. (Sections 37-40 1)
9. Symplectic geometry. (Sections 41-43 1)
10. Integral invariant of Poincaré-Cartan. (Sections 44-45 1)
11. Huygens’ principle. (Section 46 1)
12. Hamilton’s equations. (Sections 47-48 1)
13. Action-angle variables. (Sections 49-50 1)
14. Averaging. (Sections 51-52 1)
Reference:
1. V.I. Arnold, Mathematical Methods of Classical Mechanics. Second Edition. Springer. 1989.
Prerequisites: Analysis I-III, Linear Algebra.
Remark: We recommend the English presentations, but German is also possible if all other participants agree.