Syllabus for Analytical Mechanics

Analytisk mekanik

Syllabus

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

    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:

    First cycle
    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.

    Second cycle
    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.

  • Grading system: Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
  • Established: 2014-03-13
  • Established by:
  • Revised: 2018-08-30
  • Revised by: The Faculty Board of Science and Technology
  • Applies from: week 30, 2019
  • Entry requirements: 120 credits with Linear Algebra II and Mechanics III.
  • 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.

Syllabus Revisions

Reading list

Reading list

Applies from: week 30, 2019

  • Goldstein, Herbert Poole, Charles P.; Safko, John Classical mechanics

    3. ed.: San Francisco: Addison Wesley, cop. 2002

    Find in the library

    Mandatory