國立清華大學數學系
天體力學導論
Math 5770-00 (Fall 2024)  Introduction to Celestial Mechanics 

Course Description

This course is a mathematical introduction to celestial mechanics. The classical celestial mechanics, also known as the Newtonian n-body problem, deals with the motions of celestial bodies governed by Newton’s law of universal gravitation. Many important concepts in dynamical systems and topology were first developed in attempts to understand the Newtonian n-body problem.

As an introductory course, we will mainly focus on the Kepler problem (n=2) and the three-body problem, and we will briefly introduce mathematical theories related to these problems. Some numerical experiments will be demonstrated and some research topics will be briefly introduced.

Topics to be covered include:
1. Introduction (Gravitation, Newtonian mechanics, Lagrangian mechanics, integrals of motions, …)
2. The Kepler problem (Kepler’s laws, Kepler equation, Lambert theorem, regularization, …)
3. The 3-body problem (restricted problem, libration points, stability, …)
4. The n-body problem (self-similar solutions, continuations, variational principles, …)

This course is intended for graduate students and advanced undergraduate students who are interested in classical mechanics and with solid undergraduate-level mathematical training. Required prerequisite knowledge includes differential equations and linear algebra. Some training in programming will be helpful. We will try to make this course as self-contained as possible.

References

1. V. Arnold, V. Kozlov, A. Neishtadt: Mathematical aspects of classical and celestial mechanics, 2nd edition, Springer-Verlag 1997.
2. R. Fitzpatrick: An introduction to celestial mechanics, Cambridge University Press, 2012. http://farside.ph.utexas.edu/teaching/celestial/Celestial/Celestial.html
3. K. Meyer, G. Hall: Introduction to Hamiltonian systems and the N-body problem, Springer- Verlag, 1992.
4. R. Moeckel: Lectures on central configurations, 2014. 
http://www.math.umn.edu/~rmoeckel/notes/Notes.html
5. C. Siegel, J. Moser: Lectures on celestial mechanics, Springer-Verlag 1971. A. Wintner: The analytical foundations of celestial mechanics. Princeton University Press, 1941.

Syllabus

Click HERE for details.
Here are some lecture notes (to be updated every 1 or 2 weeks):
Lecture 1
Lecture 2
Lecture 3
Lecture 4
Lecture 5
Lecture 6
Lecture 7
Lecture 8
Lecture 9
Lecture 10
Lecture 11
Lecture 12

Attendance

Students are expected to attend every scheduled class. It is the student's responsibility to keep informed of any announcements, syllabus adjustments or policy changes made during scheduled classes.
 

Grading

Homework assignments: 50%.
Final Project (50%). Details will be announced in classes.