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Thienhabet - Thiên Hạ Bet. Posts - MaplePrimes. We occasionally get asked questions about methods of Perturbation Theory in Maple, including the Lindstedt-Poincaré Method. Presented here is the most famous application of this method. Introduction During the dawn of the 20th Century, one problem that bothered astronomers and astrophysicists was the precession of the perihelion of Mercury. Even when considering the gravity from other planets and objects in the solar system, the equations from Newtonian Mechanics could not account for the discrepancy between the observed and predicted precession. One of the early successes of Einstein's General Theory of Relativity was that the new model was able to capture the precession of Mercury, in addition to the orbits of all the other planets. . # Original system. f := (u,epsilon) -> -1 - epsilon * u^2; omega := 1; u0, du0 := 1 + e, 0; de1 := diff( u(theta), theta, theta ) + omega^2 * u(theta) + f( u(theta), epsilon ); ic1 := u(0) = u0, D(u)(0) = du0; # Parameters.

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