Christos Efthymiopoulos (Athens)

Hamiltonian Perturbation Theory and Applications in Celestial Mechanics


A PhD course
Period: 16 January - 15 February 2019
Dipartimento di Matematica
Università di Roma "Tor Vergata"

January 18 14:00

Program (8 lectures, 2 hours each)

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.


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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