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