The students will be able to
a) study efficiently mathematical models described by dynamical systems using numerical methods.
b) realize the main concepts of dynamical systems and the novelty of the qualitative methods used to understand systems with complex evolution
c) improve their capability in complicated computations
d) apply the methods and the models of dynamical systems in various systems in Physics, Astronomy and other scientific field.
e) understand the basic methods and models of Astrodynamics for orbit computation and design.
f) be provided by skills and knoweledge for research
Course Content (Syllabus)
1. Introduction to dynamical systems and Numerical Solutions of ODE's
2. Dynamics of Oscillators, the simple pendulum, the perturbed pendulum - Poincare section
3. Introduction to Hamiltonian systems - Systems with polynomial potentials - periodic orbits
4. The 2 and N-body problem
5. Satellite and spacecraft orbits - orbital elements - orbital transfers
6. The perturbed two-body problem
7. The restricted three body problem - Spacecraft orbits and Asteroids
8. The general 3-body problem - dynamics of planetary systems
Dynamical Systems, Chaos, Computational methods, Astrodynamics, Celestial Dynamics