The book is addressed to astronomers, astrophysicists, applied mathematicians and physicists. The needed prerequisites are calculus and differential equations at intermediate level, and celestial mechanics at undergraduate level. The information extends from classical to modern, new directions of research being indicated through a well documented bibliography. The mathematical models are singled out with clarity, as well as the tools needed to solve the problems.
The first volume, published in 1996, contains five chapters devoted to Hamiltonian mechanics, two-body, \(N\)-body, three-body problems, as well as to the study of orbits for special potentials. The present volume contains further basic mathematical models in astronomy and astrophysics. Chapter 6 is devoted to classical perturbation theory, which was created especially for celestial mechanics; it is applied to such problems as the motion around an oblate planet or Kepler’s problem with drag. The theory of perturbations contains also canonical perturbations, which are exposed in chapter 7, arriving up to the KAM theorem. Along these lines is also chapter 8 devoted to the use of Lie transform. Chapter 9 treats the theory of adiabatic invariants, which has originated from early quantum mechanics and has astronomical applications. Periodic orbits (starting from the restricted three-body problem to the general case) and resonances are the topics exposed in chapter 10, while the next chapter contains the modern developments of the theory of chaos in conservative systems. The last chapter 12 emphasizes the role of numerical methods, which nowadays permit long-time integrations and explorations of chaotic phenomena. The book ends with extensive and useful bibliographical notes, a name index, and a subject index. It is didactically written and contains topics from classical to most modern ones, treated rigorously by indicating where complete proofs are to be found.
For Volume 1 see [Zbl 1372.70003].