Dimecres 22 de maig se celebrarà una xerrada del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Conferenciant: José Lamas Rodríguez.
Universitat / Institut de recerca: Universitat Politècnica de Catalunya.

Data: Dimecres, 22 de maig de 2024.
Hora: 13:00, pausa pel cafè; 13:20, xerrada.
Lloc: UPC (FME aula 103) i Zoom.
Idioma: Anglès.

Títol: Collision leading to chaos in the restricted 3-Body Problem.

Resum: We consider a very important problem in the field of celestial mechanics, called the restricted planar circular three-body problem. In this setup, we are examining how a small, massless object moves under the gravitational influence of two larger bodies, which are orbiting each other in circular trajectories around a common center. When we look at this problem in the right mathematical framework, we find that it is governed by what are called Hamiltonian dynamics, which essentially means that energy is conserved. This energy is often referred to as the Jacobi constant. For our interest, we will focus on the so called ejection-collision orbits. These are trajectories where the small object starts off near one of the bigger bodies, gets flung out into space for a while, and the comes crashing back into it. We are going to explore how we can create these orbits, especially when the masses involved are really lopsided. We introduce some mathematical concepts, like the stable and unstable manifolds, which help us understand where these orbits come together. Essentially, we are going to show that for certain conditions, there are points where the trajectories of these orbits
intersect in a particular way, leading to different kind of behaviour.