Learning Outcomes
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 (flows and discrete maps)
2. Computational procedures - Numerical solution of differential equations - repeating procedures
3. Non linear systems. Computation of Orbits - Equilibriums and stability. bifurcation, limit cycles, chaos
4. Oscillators, the simple pendulum, the perturbed pendulum - Poincare section
5. The standard map - fixed points, stability, homoclinic chaos
6. Introduction to Hamiltonian systems - Systems with polynomial potentials - periodic orbits
7. Dynamics in our Solar system - The two body problem - Satellites
8. The restricted three body problem - Spacecraft orbits - Asteroid and planetary orbits
Keywords
Dynamical Systems, Chaos, Computational methods, Astrodynamics, Celestial Dynamics