(Created 2011-09-01.)
 ANALYTICAL MECHANICS FMEN15
Credits: 7,5. Grading scale: TH. Cycle: A (Second Cycle). Main field: Technology. Language of instruction: The course might be given in English. Optional for: F4, F4tf. Course coordinator: Associate Prof. Per Lidström, per.lidstrom@mek.lth.se, Mechanics. Recommended prerequisits: Basic courses in Engineering Mechanics, Linear Algebra and Calculus. Assessment: Hand in exercises and written exam. Home page: http://www.mek.lth.se.

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.

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.

Skills and abilities
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.

Literature
Goldstein, Poole & Safko: Classical Mechanics. 3rd ed. Addison Wesley. 2002.
Lidström P.: Lecture Notes on Analytical Mechanics. Div. of Mechanics. Lund University. 2007