2006, Vol.9, No.2, pp.115-124
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, Poincaré 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 Poincaré surfaces of
section.
Key words:
phase space structure, invariant sets, Poisson sphere,
enveloping surfaces, bifurcations, Poincaré sections
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