(Created 2008-07-17.)

ANALYTICAL MECHANICS | FMEN15 |

**Aim**

- give basic knowledge about the principles, the conceptions and methods in analytical mechanics based on Langranges and Hamiltons 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 Langranges and Hamiltons 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**

Lagranges method: mechanical systems, degrees of freedom, generalized coordinates, the Lagrangian, variational principles, Euler-Lagranges equations, cyclic coordinates, constants of motion, Noethers theorem. Hamiltons method: canonical momenta, Legendre transformation, phase space, the Hamiltonian, Hamiltonian dynamics, Liouvilles theorem, canonical transformations, the Poisson bracket, integral invariants, transformation theory, integrable systems, action-angle variables. Hanilton-Jacobis 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