Abstract
The nonlinear response of a three degree of freedom vibratory system with double pendulum in the neighbourhood internal and external resonances is investigated. The equations of motion have bean solved numerically. In this type system one mode of vibration may excite or damp another one, and for except different kinds of periodic vibration there may also appear chaotic vibration. To prove the character of this vibration and to realise the analysis of transitions from periodic regular motion to quasi-periodic and chaotic, the following have been constructed: bifurcation diagrams and time histories, phase plane portraits, power spectral densities, Poincaré maps and exponents of Lyapunov. These bifurcation diagrams show many sudden qualitative changes, that is, many bifurcations in the chaotic attractor as well as in the periodic orbits.
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Sado, D., Gajos, K. Note on Chaos in Three Degree of Freedom Dynamical System with Double Pendulum. Meccanica 38, 719–729 (2003). https://doi.org/10.1023/A:1025825224440
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DOI: https://doi.org/10.1023/A:1025825224440