Red uction of nonlinear dynamic systems by phase space analysis

Abstract

We look directly into the phase space of experimental or numerical data to derive nonlinear equations of motion. Our example is the dynamics of viscous droplets. While the smallest useful dimension of phase space turns out to be three, we apply methods to visualize four, five, six dimensions and more. These methods are Poincare sections and condensation of variables. The resulting equations of motion are extremely simple but nevertheless realistic.