Review of Hamiltonian mechanics. Integrability, first integrals, simmetries. Non-integrability, instability, chaos. Analytical and numerical methods for the study of Hamiltonian dynamical systems. Two-body problem. Three-body problem. N-body problem. Motion in assigned potentials.
The course aims at providing the students with an introduction to the problem of N self-gravitating bodies. Applications in Celestial Mechanics and Galactic Dynamics are shown.
KNOWLEDGE AND UNDERSTANDING ABILITY:
Students must have a thorough understanding of the most important theories of analytical mechanics and related application problems.
They must also have a good knowledge of the state of the art in at least one of the
areas of perturbation theory. The verification of knowledge and comprehension skills is done through written and oral tests.
ABILITY TO APPLY KNOWLEDGE AND UNDERSTANDING:
Students must be able to identify the essential elements of a
problem of dynamics also complex and knowing how to model it, making the necessary approximations.
They must be able to adapt existing models to new N-body systems.
Students must be able to perform analytical calculations or numerical simulations on their own. Develop the ability to perform bibliographic searches and to select interesting materials, in particular on the WEB.
These skills are acquired during the study for exam preparation, deepening some specific topics also with the reading of articles in scientific journals.
Students must be able to work in an interdisciplinary group.
Be able to present your study or the results of a bibliographic search to a specialist audience.
Students must be able to tackle new applications of the theory through a self-study.