Hamiltonian mechanics

Uitgebreide vaknaam	Hamiltonian mechanics
Leerdoelen	At the end of the course, the student is able to: 1) understand classical mechanics from the Newtonian, the Lagrangian and Hamiltonian point of view in terms calculus on manifolds 2) understand symplectic geometry and how it relates to the description of mechanical systems 3) understand the concept of integrable system and its centrality in perturbation theory 4) deal with concrete mechanical examples in this way, from modelling to describing the geometry of the solutions 5) deepen and broad the mathematical background
Omschrijving	Mathematical aspects of classical mechanics will be developed from the point of view of Hamiltonian systems, which most naturally live on symplectic manifolds. The entire theory, including a discussion of Newtonian and Lagrangian mechanics, the benefits of the symplectic formalism is illustrated with many examples, eventually touching on current research topics.
Uren per week
Onderwijsvorm	Bijeenkomst (S), Hoorcollege (LC), Opdracht (ASM)
Toetsvorm	Opdracht (AST), Presentatie (P), Verslag (R) (Each student will be in charge of a topic, preparing lecture notes, a lecture (in the form of a seminar) and an exercise for the rest of the class to discuss and solve in class. The final grade will be 50% lecture, 30% lecture notes, 20% solutions of exercises and interaction in class and forums. The evaluation form is available on the nestor page of the course.)
Vaksoort	master
Coördinator	dr. M. Seri
Docent(en)	dr. M. Seri
Verplichte literatuur	Titel Auteur ISBN Prijs Lecture notes on Hamiltonian mechanics. The notes will be made available via Nestor and are always available from https://github.com/mseri/hammech20/releases/ M. Seri Optional: Mathematical Physics: Classical Mechanics. Springer-Verlag. Institutional access to electronic version via SpringerLink. DOI: 10.1007/978-3-662-55774-7 Online ISBN: 978-3-662-55774-7 2018 A. Knauf 978-3-662-55772-3 Optional: Mathematical Methods of Classical Mechanics. GTM 60, Springer- Verlag. DOI 10.1007/978-1-4757-2063-1 2 1989 V.I. Arnold 978-1-4419-3087-3
Entreevoorwaarden	Knowledge assumed: good knowledge of Multivariable Analysis, Ordinary Differential Equations and being acquainted with Analysis on Manifolds, against a general bachelor background in mathematics. Mechanics is not required, but is of course useful.
Opmerkingen
Opgenomen in	Opleiding Jaar Periode Type MSc Courses for Exchange Students: AI - Computing Science - Mathematics - semester II a MSc Mathematics and Physics (double degree)  (Mathematics and Complex Dynamical Systems (40 ects)) - semester II a keuzegroep MSc Mathematics: Mathematics and Complex Dynamical Systems - semester II a keuzegroep MSc Mathematics: Science, Business and Policy  (Science, Business and Policy: Mathematics and Complex Dynamical Systems) - semester II a keuzegroep MSc Physics: Quantum Universe  ( Keuzevakken in Theoretical Physics) - semester II a keuze: TP