In our paper A Reduction Method for Higher Order Variational Equations of Hamiltonian Systems, we illustrate our reduction algorithm by presenting a full reduction for the classical hard case of the Henon-Heiles system (where a third variational equation is needed in order to prove non-integrability).

The Maple calculations may be reproduced (and checked) using this file (click here).

The file contains : Maple code used in the calculations, then the necessary matrices (the variational equations), and then the reduction process in detail.