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Vorlesung: Einführung in die Himmelsmechanik - Details
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Veranstaltungsname Vorlesung: Einführung in die Himmelsmechanik
Untertitel Introduction to Celestial Mechanics
Veranstaltungsnummer MTH-3290
Semester WS 2021/22
Aktuelle Anzahl der Teilnehmenden 12
Heimat-Einrichtung Analysis und Geometrie
Veranstaltungstyp Vorlesung in der Kategorie Lehre
Erster Termin Montag, 18.10.2021 14:15 - 15:45, Ort: (Zoom)
Online/Digitale Veranstaltung Veranstaltung wird online/digital abgehalten.
Hauptunterrichtssprache englisch

Räume und Zeiten

(Zoom)
Montag: 14:15 - 15:45, wöchentlich (14x)

Kommentar/Beschreibung

This is an introduction to the mathematical theory of celestial mechanics.

Since the foundamental work of Sir Issac Newton, the Newtonian N-body problem were important topics of science for centuries, both for theoretical interests and for practical purposes. While the two-body problem is a highly symmetric integrable system, the geometry and dynamics of the three-body problem are already highly complicated, and the phenomenon of deterministic chaos already appear: an extremely small difference of initial data will lead to a drastic difference of orbits after a sufficiently long time. These systems also serve as natural examples of symmetric Lagrangian/Hamiltonian systems.

In this course, we shall present some fundamental theory of the N-body problem with in particular a detailed study of the two-body problem, its solutions, symmetries and some ways to eliminate the singularities of two-body collisions. We shall then focus on the applications of variational methods to this problem which allow to identify interesting periodic orbits.