From a mathematical point of view classical mechanics combines a great variety of mathematical objects, such as differential equations, manifolds, Lie groups and Lie algebras, variational calculus, symplectic geometry and ergodic theory. In physics motion of objects is described by differential equations, but as we will see the solutions of these equations, i.e. the trajectories of our objects in phase space, are integral curves of a vector field defined on phase space. This vector field is determined by a differential two form (called symplectic form) and the energy function (called Hamiltonian function). We will therefore find that phase space actually is a symplectic manifold. From there we can go in many directions. A selection of possible topics can be found here.

Every student gives a talk on a subject he chose and actively participates in the other talks. Everyone also needs to write a summary of his talk that will be uploaded to the homepage. If there are two students interested in the same topic they can give the talk together. In the next weeks we will make suggestions on suitable literature for the topics of the talks, but every student should feel free to also study and present other sources. A selection of possible topics can be found here. We do not need to cover all of them and we can easily split some of them into two or three talks. The different topics are supervised by three different tutors, if you are interested in giving a talk please contact the tutor responsible for the topic. Below you can find a provisional schedule, but adjustments depending on topics and order are still possible. The talks will be mondays 2pm and online via zoom, the link is

https://us02web.zoom.us/j/81319265190?pwd=OFRFRVhseVNRQ3p0NGZBeWlyK2EyZz09

- 02.11.2020 (Carlota Dencker Castro-Rial): Phase Space and Newtons Law
- 09.11.2020 (Robert Weiß/ Lennart Bürger): Basics on Manifolds
- 16.11.2020 (Morten Will): Calculus of Variation and Lagrangian Formalism
- 23.11.2020 (Daniel Tieck): Hamiltonian Formalism
- 30.11.2020 (Joran Köhler): Rigid Body
- 07.12.2020 (Sebastian Pitz): Symmetries and Noether’s theorem
- 14.12.2020 (Lucas Freitag): Arnolds Theorem 1
- 11.01.2021 (Niclas Göring): Arnolds Theorem 2

- 18.01.2021 (Nikolas Uesseler/Yannis Riedel): Magnetic Systems
- 25.01.2021 (Joachim Stein/Gloria Elena Garcia Garcia ): Chaos with the Example of the Double Pendulum
- 01.02.2021 (Martin Gonzalez): Billiards
- 08.02.2021 (Antonia Seifert/ Leonardo Valle): Three-Body Problem and n-Body Problem
- 15.02.2021 (Hannes Keppler/Tobias Krebs): Classical Field Theory
- 22.02.2021 (Niklas Emonds): Introduction to Geometric Quantization

- [Ar] V. I. Arnold, Mathematical methods of classical mechanics
- [AM] Ralph Abraham and Jerrold E. Marsden, Foundation of Mechanics
- [Au] Michèle Audin, Spinning tops, A course on integrable systems
- [CH] Vicente Cortés and Alexander S. Haupt, Mathematical Methods of Classical Physics
- [dS] Ana Canas da Silva, Lectures on Symplectic Geometry
- [FvK] Urs Frauenfelder and Otto van Koert, The Restricted Three-Body Problem and Holomorphic Curves
- [Fo] I.M. Gelfand and S.V.Fomin, Calculus of Variations
- [Kn] Andreas Knauf, Mathematical Physics: Classical Mechanics
- [Ha] Brian C. Hall, Quantum Theory for Mathematicians