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978-0-8176-4595-3

Integrable Systems in Celestial Mechanics

Publication Date: 2008

ISBN: 978-0-8176-4595-3

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This work presents a unified treatment of three important integrable problems relevant to both Celestial and Quantum Mechanics. Under discussion are the Kepler (two-body) problem and the Euler (two-fixed center) problem, the latter being the more complex and more instructive, as it exhibits a richer and more varied solution structure. Further, because of the interesting investigations by the 20th century mathematical physicist J.P. Vinti, the Euler problem is now recognized as being intimately linked to the Vinti (Earth-satellite) problem. Here the analysis of these problems is shown to follow a definite shared pattern yielding exact forms for the solutions. A central feature is the detailed treatment of the planar Euler problem where the solutions are expressed in terms of Jacobian elliptic functions, yielding analytic representations for the orbits over the entire parameter range.


Subject: Mathematics and Statistics, Euler problem, Kepler problem, Lagrangian mechanics, Potential, Vinti problem, calculus, differential equation, earth-satellite problem, mathematical physics, two-body problem, two-fixed center problem