Course syllabus

# Analytisk mekanik

Analytical Mechanics

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

## General Information

## Aim

## Learning outcomes

## Contents

## Examination details

## Admission

## Reading list

## Contact and other information

Analytical Mechanics

Valid for: 2022/23

Faculty: Faculty of Engineering, LTH

Decided by: PLED M

Date of Decision: 2022-04-07

Language of instruction: The course will be given in English

- 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.

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.

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.

Grading scale: TH - (U,3,4,5) - (Fail, Three, Four, Five)

Assessment: Hand in exercises and written exam.

The examiner, in consultation with Disability Support Services, may deviate from the regular form of examination in order to provide a permanently disabled student with a form of examination equivalent to that of a student without a disability.

Assumed prior knowledge: Basic courses in Mechanics, Linear Algebra and Calculus in One Variable and Several Variables.

The number of participants is limited to: No

The course might be cancelled: If the number of applicants is less than 12.

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

Course coordinator: Solveig Melin, solveig.melin@mek.lth.se

Course homepage: http://www.mek.lth.se