Main field(s) of study and in-depth level:
Explanation of codes
The code indicates the education cycle and in-depth level of the course in relation to other courses within the same main field of study according to the requirements for general degrees:
G1N: has only upper-secondary level entry requirements
G1F: has less than 60 credits in first-cycle course/s as entry requirements
G1E: contains specially designed degree project for Higher Education Diploma
G2F: has at least 60 credits in first-cycle course/s as entry requirements
G2E: has at least 60 credits in first-cycle course/s as entry requirements, contains degree project for Bachelor of Arts/Bachelor of Science
GXX: in-depth level of the course cannot be classified.
A1N: has only first-cycle course/s as entry requirements
A1F: has second-cycle course/s as entry requirements
A1E: contains degree project for Master of Arts/Master of Science (60 credits)
A2E: contains degree project for Master of Arts/Master of Science (120 credits)
AXX: in-depth level of the course cannot be classified.
Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
The Faculty Board of Science and Technology
120 credits with Linear Algebra II and Mechanics III.
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.