Department of Physics

18903 Dynamical Αstronomy

Course Webpage: https://eclass.uoa.gr/courses/PHYS376/

Course Content

• Basic elements of the theory of orbits: Motion in a central gravitational field. Orbits in axisymmetric gravitational potentials.
• The basic theory of Hamiltonian dynamical systems: Action-angle variables, Poisson brackets, canonical transformations and Lie theory. Birkhoff normal form, Integrals of motion and adiabatic invariants. KAM theory and Nekhoroshev theory.
• Chaos in Hamiltonian dynamical systems: Surfaces of section. Periodic orbits. Bifurcations and stability of periodic orbits. Invariant tori and rotation numbers. Invariant manifolds. Lyapunov Characteristic Numbers. Homoclinic and Heteroclinic Chaos. Kolmogorov-Sinai Entropy.
• The restricted three-body problem: Circular restricted three-body problem – stability of the equilibrium points, the regularization of the circular restricted three-body problem. Extensions and generalizations of the circular restricted three-body problem.
• The N-body problem: Equations of motion. The integrals of motion. Virial theorem. Particular solutions of the N-body problem.
• The dynamics of small bodies in the solar system and dynamics of the extrasolar planetary systems: Chaos in the circular restricted three-body problem and applications in the solar system and the extrasolar planetary systems – Motion close to the stable Lagrangian points and Trojan asteroids and planets - Motion close to the unstable Lagrangian points and the capture of comets. The rotation of Hyperion. The Kirkwood gaps. The Neptune-Pluto system.
• Galactic and stellar dynamics: Elements of stellar dynamics. Chaos in 2D and 3D rotating galactic Hamiltonian systems. Orbits in triaxial galactic potentials. Orbits and resonances in galactic discs. Dynamics of the Milky Way.