Group Analysis of Differential Equations and Integrable Systems − 2018

Luc Haine (Universit├ę catholique de Louvain, Louvain-la-Neuve, Belgium)

On a generalization of Jacobi's Elegantissima

Jacobi's Elegantissima is a formula which expresses the maximum angle of oscillation of a pendulum in terms of the period of oscillation. We shall present a generalization of this formula due to the famous Belgium cosmologist Georges Lemaître, back in 1956. Another instance of this formula appears in a paper by Gerald Witham in 1984, about the famous cnoidal wave which solves the Korteweg-de Vries equation.