Dear all,
we are happy to invite you to the next session for the SIJIMat (Seminari Interdisciplinari per a Joves Investigadors en Matemàtiques):
Collision leading to chaos in the restricted planar three-body problem
? José Lamas Rodriguez (Universitat Politècnica de Catalunya)
? 04/04/2024
? 12h
?Aula Petita CRM
? After the seminar, pizza will be offered to participants of the Seminar
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ABSTRACT
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.
SPEAKER
José Lamas Rodriguez
Predoctoral Researcher at Universitat Politècnica de Catalunya (UPC)
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