Mechanics and Symmetry

What it is about

You will learn mathematical foundations of mechanics with a focus on symmetries: multilinear algebra, differential geometry and Lie groups, variational principles and reduction (Euler–Poincaré), as well as related structures such as symplectic geometry and Lie–Poisson brackets. In the end you will be able to apply variational principles, perform reduction for symmetric systems, and assess conservation laws using momentum maps/Noether arguments.

What you will be able to do

• Understand systems on Lie groups and their symmetry properties
• Interpret and apply variational principles of mechanics
• Cite and apply Euler–Poincaré reduction
• Compute momentum maps and verify their conservation via symmetry

What the module consists of

• VorlesungTransmission of theoretical foundations (Whiteboard, occasionally slides)
• Gruppenarbeit/ProjektWorking on tasks in groups with a report and presentation

Teaching method

• Whiteboard-VorlesungExplanation and derivation of concepts
• Folienpräsentation (gelegentlich)Support and structuring of topics