Syllabus for Analytical Mechanics
- 5 credits
- Course code: 1FA163
- Education cycle: Second cycle
Main field(s) of study and in-depth level:
- Grading system: Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
- Established: 2014-03-13
- Established by:
- Revised: 2022-10-13
- Revised by: The Faculty Board of Science and Technology
- Applies from: Autumn 2023
120 credits in science/technology with Linear Algebra II. Participation in Mechanics III. Proficiency in English equivalent to the Swedish upper secondary course English 6.
- Responsible department: Department of Physics and Astronomy
On completion of the course, the student should be able to:
- derive the Hamilton formalism from the Lagrange formalism and vice versa
- analyse the motion of a system using phase portraits
- derive the canonical transformations and relate these to a generating function
- explain the notion of constants of the motion and their relation to cylic variables as well as derive Hamilton-Jacobi theory from this point of view
- define and analyse definiera action-angle variables for integrable systems
- give a qualitative account of critical points, stability and the KAM theorem
- apply time(in)dependent perturbation theory to simple systems
- describe the basics of qualitative dynamics and Chaos theory.
Canonical formalism: Hamiltonian. Canonical equations. Phase portraits. Canonical transformations. Poisson brackets and conservation laws. Liouville's Theorem. Hamilton-Jacobi method: Hamilton-Jacobi equation. Separation of variables. Action-angle variables. Adiabatic invariants.
Qualitative behaviour of Hamiltonian systems: Canonical perturbation theory. Chaotic and integrable systems. Kolmogorov-Arnold-Moser Theorem. Chaos in the Solar system. Example of integrability: Calodgero-Moser system.
Lectures and tutorials.
Written examination. In addition there are hand-in problems. Credit points from these are included only in the regular exam and the first regular re-exam.
If there are special reasons for doing so, an examiner may make an exception from the method of assessment indicated and allow a student to be assessed by another method. An example of special reasons might be a certificate regarding special pedagogical support from the disability coordinator of the university.
The course may not be included in the same higher education qualifications as 1FA154 Analytical mechanics and special relativity.
The reading list is missing. For further information, please contact the responsible department.