Classical Mechanics

Description

For thirty years this has been the acknowledged standard in advanced classical mechanics courses. This classic book enables readers to make connections between classical and modern physics - an indispensable part of a physicist's education. In this new edition, Beams Medal winner Charles Poole and John Safko have updated the book to include the latest topics, applications, and notation, to reflect today's physics curriculum. They introduce readers to the increasingly important role that nonlinearities play in contemporary applications of classical mechanics. New numerical exercises help readers to develop skills in how to use computer techniques to solve problems in physics. Mathematical techniques are presented in detail so that the book remains fully accessible to readers who have not had an intermediate course in classical mechanics. For college instructors and students.

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)

Velocity-dependent Lagrangians (i.e., those with "external terms," as Santilli calls them) are discussed in §1-5 (pp. 25ff.).