國立清華大學數學系
天體力學導論
Math 57700-00 (Fall 2013) Introduction to Celestial Mechanics
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Office: 綜三 609 |
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 focus mainly on the Kepler problem (n=2) and the three-body problem.
Numerical experiments (using C++, Mathlab, Mathematica) will be demonstrated in
classes and several 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, variational properties, …)
3. The 3-body problem
(restricted problem, lunar and satellite orbits, libration points, …)
4. The n-body problem
(self-similar solutions, variational constructions, stability, …)
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.
Primary
References:
1. V. Arnold: Mathematical
Methods of Classical Mechanics, Springer-Verlag 1989.
2. V. Arnold, V. Kozlov, A.
Neishtadt: Mathematical aspects of classical and celestial mechanics, 2nd
edition, Springer-Verlag 1997.
3. R. Fitzpatrick: An
introduction to celestial mechanics, Cambridge Univ. Press, 2012.
4. C. Siegel, J. Moser:
Lectures on celestial mechanics, Springer-Verlag 1971.
5. K. Meyer, G. Hall:
Introduction to Hamiltonian Systems and the N-body Problem, Springer-Verlag,
1992.
Grading:
Homework assignments: 50%
Final exam (oral
presentation and final project): 50%
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.