Orbits in spherical potentials:
Binney and Tremaine 3.1 (new), 3.1 (old)
For discussions of orbits in spherical potentials, you can also look at just
about any undergraduate mechanics book.
Integrals of motion:
Binney & Tremaine 3.1.1 (new), 3.1.1 (old)
Binney & Tremaine, Appendix F (new), Appendix 1.E (old)
The best derivation of the equations of fluid mechanics is Landau
and Lifshitz, Fluid Mechanics. Everything you need is derived
by page 4!
Collisionless Boltzmann equation:
Binney & Tremaine 4.1 (new), 4.1 (old)
The reason for using the cumbersome name "collisionless Boltzmann
equation" rather than the simple "Vlasov equation" is described