Coloquio de Estudiantes de Postgrado 14/04/21

Actualizado: Puedes ver la charla acá VER CHARLA EDWARD TURNER



Este miércoles inicia el Coloquio de Estudiantes de Postgrado en Matematica y Ciencias aplicadas UBB con la charla del reciente Magister de nuestro departamento Mg. Edward Turner.

Reduction and Relative Equilibria in Full Gravitational N-Body Problem
Expositor : M. Sc. Edward Allan David Turner Vilches
Institucion : Universidad del Bío-Bío, Concepción, Chile
F echa : Miércoles 14 de abril de 2021
Lugar : Zoom meeting (ID 821 7483 4254, Password 484062)
Enlace : zoom
Hora : 19:00PM -20:00 PM (Santiago Time).

Abstract. We study the rota-orbital dynamics of N finite well-defined bodies under gravitational inter- action. This problem is known as the full gravitational N-body problem obtained after elimi- nating the assumption of punctual masses in the classical N-body problem. We prove that the Newton-Euler equations of motion for this problem are Hamiltonian.
Using the natural symmetries, translations, and rotations, we reduce by six the number of degrees of freedom. Moreover, we compute the reduced spaces, and we show that the translational-reduced space and the rotational-reduced space are both given as non-canonical Hamiltonian systems. Furthermore, we give a detailed description of the generated Poisson structure at each stage of the reduction process. Our analysis found that the total angular momentum and the orthogonality conditions of SO(3) are the Casimir functions. By considering the translational-rotational-reduced equations of motion, we characterize the relative equilibria and also classify them into two main categories; Parallel and Non-Parallel equilibria.
Among the parallel equilibria, we and the clas- sical Lagrangean and non-Lagrangean equilibria. For N>2, there is one more new type of equilibria which will be dubbed semi-Lagrangean, the latter being original from this research.

keywords: Rigid body, reduction, relative equilibria and roto-orbital dynamics.