where E = T + V is the conserved energy and the γ γ s are constants. As described below, the variables have been changed from q s to φ s, and the functions u s and w s substituted by their counterparts χ s and ω s. This solution has numerous applications, such as the orbit of a small planet about two fixed stars under the influence of Newtonian gravity. The Liouville dynamical system is one of several things named after Joseph Liouville, an eminent French mathematician.