If you know Russian, there is very helpful book of A.P. Markeev "Libration points in cosmic dynamics" (1978). In chapter 3, paragraph 1 you can find theory of reducing Hamiltonian system to normal form of Birkhoff's type. Also you can find there an information about stability analysis in Lyapunov sense, if you need.

Thank you very much !! I have found the book. Even though I do not know Russian, I can understand the main ideas within the chapter which you have recommended. It is really useful.

I recommend the books "Solar System Dynamics" by Murray & Dermott and "Methods of Celestial Mechanics" by Brouwer.

Professor Nogueira,

Thank you very much for your suggestions. I will acquire those books and consult them.

Vlad.

It seems to me that there were a few papers published in the Journal of Celestial Mechanics (before it was renamed Celestial Mechanics and Dynamical Astronomy) on this topic.  I believe this goes back to the 1970-73 time frame.  The beginning of this time is approximately the same as Andre Deprit's 1970 paper on the main problem in artificial satellite theory.

Professor Cefola! What a surprise to meet here in the ResearchGate community!

Thank you very much for your suggestion. I have found the aforementioned papers. They are authored by Ahmed Aly Kamel, apparently one of André Déprit's scholars in the US. The key concept is the Lie transform, which is not confined to the symplectic manifolds associated to conservative systems, but may be applied to any system of differential equations. I will digest, assimilate and try to make use of this concept.

Respectfully,

Vlad.

The book by Nayfeh, 'Perturbation Methods' from the 1970's gives a good  practical summary of many lf these methods. Please check it out.

Regards