Course syllabus

# Analytisk mekanik Analytical Mechanics

## FMEN15, 7,5 credits, A (Second Cycle)

Valid for: 2016/17
Decided by: Education Board E
Date of Decision: 2016-04-04

## 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