c © 2006 Nonlinear Phenomena in Complex Systems Regular and Chaotic Rigid Body Dynamics

Rigid body dynamics is taught in mechanics courses as the highlight of non-trivial integrability. Yet the overwhelming majority of problems in the field is non-integrable. The beautiful methods of integration developed by the heroes Euler, Lagrange, Jacobi, Weierstraß, Kovalevskaya, Poincare ́ and others, distract from the fact that chaos rather than regularity is the rule, and that numerical as well as graphical methods ought to be developed to exhibit the system’s true complexity. The paper describes attempts in that direction, focusing on the identification of invariant sets in configuration and momentum space, and on the definition of convenient Poincare ́ surfaces of section