musgravepeter

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.

+1 for Artin's Algebra. I think is very under appreciated.

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.

Snap. I am also a physicist trying to learn math. In my case it's:

- Introduction to Analysis (Mattuck)

- Elementary Differential Geometry (Pressley)

both chosen because they have solutions in the book, which I find important for self-study.

Also just got (hot off the presses)

Visual Differential Geometry and Forms (Needham)

Looks fantastic!

Topology is next on the list...

Steinhardt's book "The second kind of impossible" describes his involvement with quasi-crystals. It's very worthwhile.