# Syllabus for Analytical Mechanics

Analytisk mekanik

• 5 credits
• Course code: 1FA163
• Education cycle: Second cycle
• Main field(s) of study and in-depth level: Physics A1N
• 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
• Entry requirements:

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

## Learning outcomes

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.

## Content

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.

## Instruction

Lectures and tutorials.

## Assessment

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.

## Other directives

The course may not be included in the same higher education qualifications as 1FA154 Analytical mechanics and special relativity.