I have to give a 30 mins lecture this coming Thursday in my classical mechanics class (graduate level in math department, with Arnold as the primary text) and I am really struggling to find any good literature on the subject of the title.
My professor says that Goldstein "should have" material on this subject.... but it just doesn't, what it does have is about 3/4 of a page on hyperbolic motion in the theory of special relativity (not what I was asked to discuss). I did give a read over "Analytic Methods" by Hand and Finch (an undergrad text) and it $does$ develope some ideas, but it is a bit to shallow and further the style is a bit foreign to me (clearly a text written for physicists).
I really enjoy the style of Arnold's mechanics text, so if anyone could recommend something that would be at that level and possibly of that style that absolutely does have hyperbolic motion in a central field that would be greatly appreciated, also any good papers would be nice as well.
The following paper is a good example of the level of sophistication I would like (and can handle): http://mae.nmsu.edu/~asanyal/Sanyal_res/CDSS100107.pdf unfortunately, it also completely avoids the paticular case of hyperbolic motion.
I thought preparing for this talk would be a trip to the library and a search on Google, but it's turning out much more complicated than that. Please keep in mind this is my first physics course, thank you. Apologies if this is an inappropriate place to put this question (if so, please suggest where I can move it to).