A PhD course
Program
(8 lectures, 2 hours each)Period: 16 January - 15 February 2019 Dipartimento di Matematica Università di Roma "Tor Vergata" Schedule:
1. A `Warm-up' example: pendulum with external forcing 2. Hamiltonian flow - symplectic transformations - Lie series 3. Birkhoff normal form for the pendulum wih external forcing 4. Resonances and Chaos 5. Heuristic discussion of the Kolmogorov - Arnold - Moser and Nekhoroshev Theorems 6. Application to Celestial Mechanics I: Secular theory for planetary motions 7. Application to Celestial Mechanics II: Resonances for Earth satellites 8. Application to Celestial Mechanics III: Rotational motions of celestial bodies Students will be assigned with projects requiring use of some tools of computational algebra. A tutorial on such tools will be provided during the course. Abstract
After a quick review of the basics of the Hamiltonian formalism, the course will focus on methods of canonical perturbation theory allowing to characterize by analytical means the dynamics in nearly-integrable Hamiltonian systems with few degrees of freedom. The cornerstones of perturbation theory (symplectic transformations, normal form theory) will be presented along with some central results in the field, outlined in a heuristic way. The applications refer to mainstream problems of modern celestial mechanics and astrodynamics. This course is part of the MIUR Excellence
Department Project awarded
to the Department of Mathematics, University of
Rome Tor Vergata, CUP E83C18000100006
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