Chapter 48 - Henripoincaré, memoir on the three-body problem (1890)

Abstract

Drawing on Poincaré work on the qualitative theory of differential equations, in the memoir on the three-body problem, Poincaré developed a theory of periodic solutions that opened up an entirely new way of thinking about dynamical problems. Although Newton had been able to use geometry to solve the two-body problem, it rapidly became clear that the three-body problem required an analytical approach. Because each of the three particles has three position components and three velocity components, the problem is a system of order 18, and it can be represented by a system of nine second order differential equations. A combination of royal patronage and carefully planned public relations meant that the competition gained recognition stretching well beyond the world of mathematics. As is often the case with such problems, its importance lies as much in the mathematical advances generated by attempts at its solution as in the actual problem itself, and since its formulation by Isaac Newton many leading mathematicians have been attracted to it.