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Info on Dynamical Systems and Sitnikov Problem

  1. Jun 30, 2010 #1
    Hey guys.

    I'll be doing my first research project with a professor and although the details are a bit unclear, he gave me the topic at hand and the problem we'll be tackling: the Sitnikov problem.

    To quote him,

    He also suggested that I should learn about the following topics:

    I'm currently working from Introduction to Hamiltonian Dynamical Systems and the N-Body Problem by Hall and Meyer. I read like the first 50 pages, then I just started picking the book apart for the stuff in the latter quotes. However, some of it is a bit unclear and some of the topics are not in the book (these are boldened), thus leaving me searching for more sources.

    I was wondering if anyone knew of any good books/pdf/article/etc. on these topics, or perhaps on the Sitnikov problem. I could use the help.
  2. jcsd
  3. Jul 1, 2010 #2
    Vladamir Arnold's Mathematical Aspects of Classical and Celestial Mechanics (NOT to be confused with Mathematical Methods of Classical Mechanics) is, by far, the most authoritative text on mechanical systems. I think he covers all of the stuff you bolded.

    In addition, Giovanni Gallavotti's Elements of Mechanics may be helpful. (Found Here: http://ipparco.roma1.infn.it/pagine/2008.html)

    A couple related articles by J. Moser comes in mind:

    J. Moser- On invariant curves of area-preserving mappings of an annulus. (1962)
    As well has his responce

    J. Moser- Remark on the paper “On invariant curves of area-preserving mappings
    of an annulus”.
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