Master’s studies

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
  • Grading system: Fail (U), 3, 4, 5.
  • Established: 2014-03-13
  • Established by: The Faculty Board of Science and Technology
  • Applies from: week 30, 2014
  • Entry requirements: 120 credits with Linear Algebra II and Mechanics III.
  • Responsible department: Department of Physics and Astronomy

Learning outcomes

A student who has successfully passed the course 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.

Other directives

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

Reading list

Applies from: week 45, 2013

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

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

    Find in the library

    Mandatory