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