This problem has been of great interest mathematically since Newton's formulation of the laws of gravity, in particular with respect to the joint motion of the sun, earth, and moon.
In 1890 it was finally published in revised form, and over the next ten years Poincaré expanded it into a monograph, Les méthodes nouvelles de la mécanique céleste [New methods in celestial mechanics].
Poincare's work led to the discovery of chaos theory,[3] set up a long-running separation between mathematicians and dynamical astronomers over the convergence of series,[4][5] and became the initial claim to fame for Poincaré himself.
This includes contributions on the singularities of solutions by Paul Painlevé, Edvard Hugo von Zeipel, Tullio Levi-Civita, Jean Chazy, Richard McGehee, Donald G. Saari, and Zhihong Xia, on the stability of solutions by Aleksandr Lyapunov, on numerical results by George Darwin, Forest Ray Moulton, and Bengt Strömgren, on power series by Giulio Bisconcini and Karl F. Sundman, and on the KAM theory by Andrey Kolmogorov, Vladimir Arnold, and Jürgen Moser,[5] and additional contributions by George David Birkhoff, Jacques Hadamard, V. K. Melnikov, and Marston Morse.
[6] Although reviewer Florin Diacu (himself a noted researcher on the n-body problem) complains that Wang was omitted, that Barrow-Green "sometimes fails to see connections ... within Poincaré's own work" and that some of her translations are inaccurate, he also recommends the book.