This paper presents theorems which establish the existence of horseshoes and Arnold diffusion for nearly integrable Hamiltonian systems associated with Lie groups. The methods are based on our two previous papers, Holmes and Marsden [1982a], [1982b]. The two main examples treated here are as follows:
- A simplified model of the rigid body with attachments. This system has horseshoes (with one attachment) and Arnold diffusion (with two or more attachments).
- A rigid body under gravity, close to a symmetric (Lagrange) top. This system is shown to have horseshoes (and hence is not integrable).
