Universitäts-Sternwarte München

Fakultät für Physik der Ludwig-Maximilians-Universität


Gravitational dynamics tutorials & seminar
Summer semester 2024

Klaus Dolag, Rhea-Silvia Remus, Tadziu Hoffmann
Andreas Burkert


Mondays, 16–18: In this class you will be required to write small computer programs to solve physical problems. This will be done incrementally in small steps, so if you have only little programming experience to date you will have the opportunity to pick this up. (Like all important skills, this will require some effort and lots of experimentation from your side.) But keep in mind that programming is not the main aspect of these tutorials — understanding physics is.


Mondays, 14–16: In addition to the tutorials, there will be a seminar in which subjects related to the tutorials will be presented. This will be before the tutorials and the goal will be to get a better understanding of the current exercise set and the related physical and numerical issues.


Information about the lecture is given on a separate web page.


For the tutorials, you will need a computer with:

  • a C/C++ or Fortran compiler (e.g., gcc or gfortran or the Intel oneAPI toolkit),
  • a text editor (such as emacs or vim),
  • a plotting program (for example, gnuplot, IDL, or Python+matplotlib).

You can also do your calculations (remotely, via ssh) on the computers of the LMU Physik CIP Pool.


Grading will be based on the seminar presentations.

Tutorial and seminar schedule


 T02024-04-15 Introduction to the shell and gnuplot
 T12024-04-22How to give a Talk Remus Units and acceleration; first program
 T22024-04-29 Gravitational forces; vectors and loops
 T32024-05-06Topic 1 / Topic 2 Karaferias / Citterio Euler integrator
 T42024-05-13Topic 3 / Topic 4 Liu / Shivaprasad Euler and other integrators


 T52024-05-27Topic 5 / Topic 6 Seidl / Strunk Kepler fitting
 T62024-06-03Topic 7 / Topic 8 N.N. / Yan Multiple (test) particles and extended potentials
 T72024-06-10Topic 9 / Topic 10Finger / Widl General 3-body problem (ejection, softening)
 T82024-06-17Topic 11 / Topic 12Kohlbach / Yang Lagrange points (restricted 3-body problem)
 T92024-06-24Topic 13 / Topic 14Zhang / R. Singh General N-body problem (free-fall collapse)
T102024-07-01Topic 15 / Topic 16N.N. / Kandekar Dynamical friction
T112024-07-08Topic 17 / Topic 18Tonelli / Lindmeir Colliding galaxies
T122024-07-15Topic 19 / Topic 20N.N. / P. Singh Visualization of galaxies in cosmological simulations

       = content updated since the tutorial class
       = new tutorial online

Seminar topics

  1. GR proofs with Galactic center dynamics
  2. General dynamics, Lagrangian formalism, equation of motion
  3. Solving ODEs
  4. Stability of the solar system
  5. Gadget-4 symplectic, hierarchical integrator
  6. Historical review: how did Kepler find his laws?
  7. Minimization algorithms for fitting
  8. Kepler, Plummer, Jaffe, Einasto, NFW, Hernquist and Co.
  9. Measuring galaxy cluster masses with phase-space methods
  10. Stable or Unstable? Orbits in the 3-body problem
  11. Ejection of stars from globular clusters
  12. Lagrange potential
  13. Of horseshoes and tadpoles
  14. Timescales in gravitating astrophysical systems
  15. The spherical collapse model
  16. Chandrasekar approach to dynamical friction
  17. Segregation of stars in globular clusters
  18. Toomre sequence
  19. Shells and streams
  20. Cosmological Simulations
Letzte Änderung 17. Mai 2024 14:58 UTC durch Webmaster (webmaster@usm.uni-muenchen.de)