Hamilton Mechanics (video lecture)
||5 credit points
||Broer, H.W. (Rijksuniversiteit Groningen)
||To develop mathematical aspects of classical mechanics via Newtonian and Lagrangian systems to the world of Hamiltonian systems, which most naturally live on symplectic manifolds. The entire theory, including the benefits of the symplectic formalism is illustrated with many examples, eventually touching on current research.
||Introduction, one and two degrees of freedom,
- The central force field, Keplers second law
- The variational principle, Euler-Lagrange
- The Legendre transformation to Hamilton-Jacobi
Noether and Liouville
- Applications to small oscillations
- The symplectic formalism
- Applications to mechanics and optics
- Averaging methods and adiabatic invariants
- Miscellaneous applications, perturbation theory
One hour and a half lecturing + one hour and a half instruction (incuding problem and homework discussion)
This course can either be followed at Rijksuniversiteit Groningen or followed on distance by means of video lectures and email contact.
In both cases, students need to register for this course. All lectures that take place at Rijksuniversiteit Groningen will be made available for students registered for this course shortly after the lecture took place. All video's will be put on Blackboard. During the course, the teacher is available for questions by email. The final exam will take place at Rijksuniversiteit Groningen.
If you choose to follow this course on a distance, by means of video lectures and email contact, you can pass this course by successfully taking the final exam at Rijksuniversiteit Groningen.
||Examination can be written, either with a quiz or by presenting an essay. The homework counts for round offs.
||V.I. Arnold, Mathematical Principles of Classical Mechanics. GTM 60, 2nd ed. Springer-Verlag 1989. To be used as a textbook and should be purchased by the students.
||Good knowledge of ordinary differential equations, against a general bachelor background in mathematics. Mechanics is not required, but is of course useful.