18 February 2020Understanding the Milky Way with Hamiltonian Mechanics

Giacomo MONARI

Observatoire astronomique de Strasbourg

I present a short summary of Hamiltonian Mechanics and how it can be used to understand the structural and kinematic properties of the Milky Way. I start with the most relevant basic notions (Hamilton’s equations, angle/action variables,…). After that, I try to convince the audience that this formalism is useful when one aims at reconstructing the mass distribution and kinematics of the stars in the Milky Way. I finally lead the audience to the Hamiltonian approach to the problem of the non-axisymmetric perturbations (bar and spiral arms) and their influence on the orbits of the stars in the Milky Way (resonant trapping, irregular orbits, orbital frequencies, etc.). In particular I will show a worked example on how such approach can help us to unveil the effects of the bar on the stars in the Galactic disk.