Abstract
By using a series of canonical transformations (Birkhoff's 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.
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Communicated by Zhu Zhao-xuan
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Fu-hua, L., Ru-jin, X. Non-integrability and chaos of a conservative compound pendulum. Appl Math Mech 13, 51–59 (1992). https://doi.org/10.1007/BF02450428
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DOI: https://doi.org/10.1007/BF02450428