Analytical Mechanics, 5 cr

The introductory video of the course for fall 2022. The contents still up to date.:
https://tuni.cloud.panopto.eu/Panopto/Pages/Viewer.aspx?id=401d3cc0-b232-415c-9868-aefc0058a942

The structure of the course

The present course aims to be a quite practical:

- Methods of Lagrangian mechanics provide a feasible toolbox for constructing equations of motion even in cases, where Newtonian mechanics proves cumbersome. How to deal with curvilinear frames of reference, accelerating coordinate systems, how to couple translation and rotation, or particles and fields?

- Hamiltonian mechanics not only deals with conservation laws and symmetries, but it also is used in constructing a bridge between classical and quantum mechanics.

- Nonlinear dynamics and chaos theory provides an excursion into how to analyze solutions of differential equations without solving them. In addition, understanding chaos, coherence and stability is useful in numerical modeling of physical systems.

- Numerical methods are integrated in the assignment part of the course (see below).

The course is implemented as

1) Lectures and group sessions. There will be only 9+1 two hour lectures or group sessions with pre-class assignments. They are intended to give an introduction to the concepts and methods used in analytical mechanics. There will be brief video recordings about the topics. The lecturer is Jouko Nieminen (jouko.nieminen@tuni.fi).

2) Assignment & exercise sessions. There are 12 exercise sessions and 6 practical assignments (with intermediate steps), for practicing problem solving techniques, going through central examples of Lagrange and Hamilton mechanics, as well as nonlinear dynamics and chaos theory. The exercise sessions are meant to be a kind of "problem solving workshop", where you can work on the problems on your own or in groups and get advice for your work, if needed. To get points from the assignments and the exercises, you need return your solutions in Moodle.