Course syllabus
Analytisk mekanik
Analytical Mechanics
FMEN15, 7,5 credits, A (Second Cycle)
Valid for: 2015/16
Decided by: Education Board E
Date of Decision: 2015-04-13
General Information
Elective for: F4, F4-tf
Language of instruction: The course will be given in English
Aim
- give basic knowledge about the principles, the conceptions and
methods in analytical mechanics based on Langrange’s and
Hamilton’s formulation of the laws of the classical
mechanics.
- provide a basis for further studies in classical mechanics and
quantum mechanics.
Learning outcomes
Knowledge and understanding
For a passing grade the student must
- provide knowledge of the most important results in the
analytical mechanics.
- be able to formulate theoretical models for mechanical systems
based on Langrange’s and Hamilton’s methods.
- have some knowledge about the relation to the classical
statistical mechanics and quantum mechanics.
Competences and skills
For a passing grade the student must
- be able to analyze some simple models for mechanical systems
using computer program (Matlab, Maple etc.).
- be able to perform an analysis of a mechanical problem and to
present the results in a well-written report.
- be able to describe some engineering problems in industrial
applications that can be studied using analytical mechanics.
Judgement and approach
For a passing grade the student must
- be able to evaluate achieved results based on the problem
formulation at hand as well as physical limitations.
Contents
Lagrange’s method: mechanical systems, degrees of freedom,
generalized coordinates, the Lagrangian, variational principles,
Euler-Lagrange’s equations, cyclic coordinates, constants of
motion, Noether’s theorem. Hamilton’s method: canonical
momenta, Legendre transformation, phase space, the Hamiltonian,
Hamiltonian dynamics, Liouville’s theorem, canonical
transformations, the Poisson bracket, integral invariants,
transformation theory, integrable systems, action-angle variables.
Hanilton-Jacobi’s method: Hamilton-Jacobi and the Schrödinger
equation. Periodic and chaotic motions. Somewhat on analytical
mechanics and its relation to classical statistical mechanics and
quantum mechanics.
Examination details
Grading scale: TH
Assessment: Hand in exercises and written exam.
Admission
Required prior knowledge: Basic courses in Engineering Mechanics, Linear Algebra and Calculus.
The number of participants is limited to: No
Reading list
- Goldstein, Poole & Safko: Classical Mechanics. 3rd ed. Addison Wesley. 2002.
- Lidström P.: Lecture Notes on Analytical Mechanics. Div. of Mechanics. Lund University. 2007.
Contact and other information
Course coordinator: Univ. lekt. Per Lidström, per.lidstrom@mek.lth.se
Course homepage: http://www.mek.lth.se