Ulf Lindstrom

Analytical Mechanics

Course Info

Litterature: Goldstein, Poole and Safko, Classical Mechanics, Third edition, Addison Wesley 2002
Examination: A 5 hour 5 problem exam. You may bring lecture notes, textbook, tables but NOT solved problems.

Course content:

The chapters from Goldstein et al that define the course are Chptrs: 8, 9, 10, (11) and 12. Chptr 11 as an orientation.

I will use the following rough outline of the lectures:

1. Lagrangian mechanics and Lagrange equations. Legendre transform. Hamiltonian. Hamilton's equations.
2. Cyclic variables. Noether's theorem and conservation laws.
3. Hamiltonian systems with one degree of freedom. Phase portraits.
4. Canonical transformations. Differentials and generating functions.
5. Poisson brackets. Relation to conservation laws and conserved quantities.
6. The Hamilton-Jacobi equation. Characteristic equation.
7. Separation of variables in the Hamilton-Jacobi equation. Relation to conservation laws.
8. Action angle variables.
9. Qualitative behaviour of Hamiltonian systems. The Kolmogorov-Arnold-Moser theorem.

Assignments: (To be handed in on wednesdays). THE FIRST ASSIGNMENT you have already done

THE SECOND ASSIGNMENT Inlupp2_2008.pdf THE THIRD ASSIGNMENT Inlupp3_2008.pdf

FOURTH ASSIGNMENT Inlupp 4 2008.pdf FIFTH ASSIGNMENT Inlupp 5 2008

Problemset: Lektion 1 Lektion 2 Lektion 3 Lektion 4 Lektion5 pdf Lektion6
Lektion 7 pdf

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Phone: 46 18 4713298

E-mail: ulf.lindstrom@teorfys.uu.se,