Mathematical Introduction to Celestial Mechanics by Harry Pollard (PDF)

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This book presents the basic mathematics underlying the subject of Celestial Mechanics. Keyed to an audience with an interest in mathematics, the book includes four major topics. Chapter 1, The Central Force Problem, deals with Kepler’s first and second laws, orbits under non-Newtonian attraction, elements of an orbit, the two-body system, the solar system, and disturbed motion. Chapter 2 introduces the n-body problem and includes the Lagrange-Jacobi formula, Sundman’s theorem on total collapse, the three-body problem, and Lagrange solutions and Euler’s solution. Chapter 3, Introduction to Hamilton-Jacobi Theory is deliberately independent of Chapter 4, Perturbation Theory.

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