Abstract: By using a series of canonical transformations(Birkhoffs series), an approximate integral of a conservative compound pendulum is evaluated. Level lines of this approximate integral are compared with the numerical simulation results. It is seen clearly that with a raised energy level, the nearly integrable system becomes non-integrable, i.e. the regular motion pattern changes to the chaotic one. Experiments with such a pendulum device display the behavior mentioned above.

Key words: conservative compound pendulum, non-integrability, chaos, canonical transformation, numerical simulation, Birkhoff’s series, normal form, nth-fold resonance