Invariant Manifolds Near L1 and L2 Points in the Restricted Three-Body Problem

Dynamical Systems Working Seminar
Friday, February 2, 2018 - 15:00
1 hour (actually 50 minutes)
Skiles 271
University of Barcelona & GT
In a given system of coordinates, the Restricted Three-Body Problem has some interesting dynamical objects, for instance, equilibrium points, periodic orbits, etc. In this work, some connections between the stable and unstable manifolds of periodic orbits of this system are studied. Such connections let one explain the movement of Quasi-Hilda comets, which describe an orbit that sometimes can be approximated by an ellipse of semi-major axis greater than Jupiter's one, sometimes smaller. Using a computer algebra system, one can compute an approximation to those orbits and its manifolds and investigate the above mentioned connections. In addition, the Planar Circular model is used as a base for the fitting of the orbit of comet 39P/Oterma, whose data were collected from the JPL Horizons system. The possibility of using other models is also discussed.