Both these books are on my book shelf and are very good. Bate et. al. especially since it is a Dover book and very affordable.
The book that is always on my DESK is "Fundamentals of Astrodynamics and Applications" by Vallado. There is also a website with code from the book for Hohmann and Lambert transfers among other things. <self-promotion>This has been indispensable in creating my Unity Asset "Gravity Engine".</self-promotion>
The article mentions "few known exact solutions". There are actually quite a number. Most are from after 1950.
Cambridge University Press has two good books:
Exact Spacetimes in Einstein's General Relativity (Griffith & Podolsky)
- good readable (if you speak GR) account of the more common solutions
Exact Solutions of Einstein's Feild Equations (Stephani, Kramer, MacCallum, Hoenstelaers, Herlt)
- encyclopedic, authoritative and mathematical. In my case an aspirational purchase
L4 and L5 are stable when the smaller mass is less than about 0.0385 times the larger mass [1]. This means e.g. a typical binary star system would not have stable L4/L5 points. The reference [1] works through this in careful detail and is an excellent reference on this topic.
[1] Solar System Dynamics, Murray and Dermott, Cambridge University Press.
I've been on a Math journey since I retired a couple of years ago and I agree with all the books mentioned that I know and look forward to picking up some of the one I do not know. I agree baby Rudin is essential, but I find it tough going.
Some books I liked for self study because they have answers:
Introduction to Analysis, Mattock.
Elementary Differential Geometry, Pressley.
There is also recently Needham's Visual Differential Geometry and Forms, which is great.
I think learning Real Analysis from baby Rudin is like learning Probability Theory from Wikipedia. It's so encyclopedic that if it's your first look at real analysis, it will be too dense to understand, but if it's your second or third look, you will find beauty in its brevity.
Very pretty book (Needham's), will check it out! I think over 20 years ago I actually attended a house party that Needham was giving in SF. It's a small world.
Agree that Baby Rudin is VERY difficult to study on its own. I recommend only studying it alongside the other two books I listed: Abbott's Understanding Analysis and Spivak's Calculus (which has a solutions manual). Abbott in particular is very straightforward (at least in comparison with baby Rudin haha)
Another point for Abbott is that it was one of the ~400 books Springer made available for free download near the start of the pandemic. I remember there were a few scripts here on HN back then to grab all those books, so many here probably already have a copy.
There is Geometric Algebra for Physicists by Doran and Lasenby (2003). It recasts mechanics, E&M up to gauge theories and GR into geometric algebra. I stalled out at mechanics but I've now taken it off the Tsundoku pile and may give it another chance.
