The Analytical Foundations of Celestial Mechanics

Description

With this 1941 monograph, Aurel Wintner joined Poincaré, Birkhoff, and others in placing celestial mechanics on a sound mathematical basis. The product of many years of work by the author, it remains an extremely valuable contribution to the literature of this field.
Starting with a review of dynamical operations, the treatment advances to local and non-local questions, dynamical systems, the problem of two bodies and the problem of several bodies, and an introduction to the restricted problem. Suitable for advanced undergraduates and graduate students of physics, the text is amply supplemented by a substantial section of notes and references in which a great deal of the historical literature from which it derives is discussed.

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from Santilli 1978 (pp. 1-2):

1. analytic formulations, e.g., Lagrange's and Hamilton's equations, Hamilton-Jacobi theory, etc.
   Whittaker (1904), Goldstein (1950), Pars (1965)
2. variational formulations, e.g., variational problems, variational principles, etc.
   Lanczos (1949), Rund (1966)
3. algebraic formulations, e.g., infinitesimal and finite canonical transformations, Lie algebras and Lie groups, symmetries and conservation laws, etc.
   Saletan and Cromer (1971), Sudarshan and Mukunda (1974).
4. geometric formulations, e.g., symplectic geometry, canonical structure, etc.
   Jost (1964), Abraham and Marsden (1967), Guillemin and Sternberg (1977)
5. statistical formulations, e.g., Liouville's theorem, equilibrium and nonequilibrium statistical mechanics, etc.
   Gibbs (1948), Katz (1967)
6. thermodynamic formulations, e.g., irreversible processes, entropy, etc.
   Sommerfeld (1956), Tisza (1966)
7. many-body formulations, e.g., stability of orbits, quadrature problems, etc.
   Wintner (1941) , Khilmi (1961), Hagihara (1970)