Classical Mechanics, Fall 2006

The lectures are in BBL 160 on Wednesdays, from 9.00 - 10.45. The exercise sessions are in the Mathematics Department K11 on Thursdays, from 10.00 - 10.45.

Course notes ``Klassieke Mechanica''

September 13
- Lectures: Sections 1.1 - 1.4 until (4.17)
- Exercises 21 September: 1.2, 1.3, 1.5
September 20
- Lectures: Sections 1.4, 1.5, the existence and uniqueness theorem in Section 2.8, Section 2.10
- Exercises 28 September: 1.7, 2.1, (1.8). The brackets mean that probably there will be no time to discuss 1.8
September 27
- Lectures: Sections 3.1, 3.2
- Exercises 5 October: 2.3, 3.1, 3.5
October 4
- Lectures: Sections 4.1, 4.2, 4.3
- Exercises 12 October: 3.6, 3.7, 3.8
October 11
- Lectures: Sections 4.4, 4.5, 4.6, 4.7, 4.8
- Exercises 19 October: 4.1, 4.2, 4.3
October 18
- Lectures: Sections 4.9, 5.1, 5.3
- Exercises 26 October: 4.4, 5.1. For exercise 5.1, read Section 5.4 on submanifolds, where you may take X equal to R^n and the tangent mapping equal to the Jacobian matrix = the matrix of first order partial derivatives.
October 25
- Lectures: Sections 5.4, 5.5, 5.6, 5.7, 5.9
- Exercises 2 November: 5.2, 5.3, 5.4. For exercise 5.4, use the first paragraph (= `alinea' in Dutch) of Section 5.12, in which it is told how to compute differential forms and their exterior derivatives in local coordinates.
November 1
- Lectures: Sections 5.10, 5.11, beginning of 5.12
- The week of November 6-10 is a break. I propose to devote the Exercise session of November 16 to a discussion of those exercises which are left over from previous sessions, due to lack of time: 1.8, 3.5, 3.8
November 15
- No lectures, due to the bus strike.
- Exercises 23 November: 3.2, 3.3, 3.4: on periodic solutions near an equilibrium point of a conservative system with one degree of freedom
November 22
- 5.12, 5.13.
- Exercises 30 November: 3.4, 7.8, 7.1 (read formula (7.4)). Please note that, in accordance with Osiris, in Block 2 the exercise session is in room BBL 160, still on Thursdays from 10 to 10.45.
November 29
- 7.1, 7.2, 7.3.
- Exercises 7 December: 7.5, 7.6, 7.7. Please note that, in accordance with Osiris, in Block 2 the exercise session is in room BBL 160, still on Thursdays from 10 to 10.45.
December 6
- 7.3, Lemma 7.3 in Section 7.5.
- Exercises 14 December: 7.7, 7.2, 7.12. In Exercise 7.2 just take for sigma the antisymmetric bilinear form on the 2n-dimensional space given by (7.14). The linear mapping L is a canonical transformation = symplectic linear transformation if and only if sigma(Lu, Lv)=sigma(u,v) for every pair of 2n-dimensional vectors u and v. In Exercise 7.12 it is easier not to write things out in coordinates.
December 13
- 7.7, 7.8.
- Exercises 11 January: 7.11, 7.13.
January 10
- 8.1, 7.4.
- Exercises 18 January: 7.3, 8.2.