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Lecture: Einführung in die Himmelsmechanik - Details
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General information

Subtitle Introduction to Celestial Mechanics
Course number MTH-3290
Semester WS 2021/22
Current number of participants 19
Home institute Analysis und Geometrie
Courses type Lecture in category Teaching
Next date Mon , 25.10.2021 14:15 - 15:45, Room: (Zoom)
Online/Digitale Veranstaltung Veranstaltung wird online/digital abgehalten.
Hauptunterrichtssprache englisch

Course location / Course dates

(Zoom) Monday: 14:15 - 15:45, weekly (14x)

Comment/Description

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.