×

zbMATH — the first resource for mathematics

The transition to chaos in a simple mechanical system. (English) Zbl 0666.70030
A simple mechanical device and its response to periodic excitation is considered. The system consists of an inverted pendulum with rigid barriers which limit the amplitude variation from the unstable upright position. The static stable rest positions correspond to the pendulum leaning against one of the barriers. When subjected to periodic excitation the system response can be quite complicated and may include one or several stable subharmonics and/or chaotic motions. The analysis presented here is based on a piecewise linear model which allows explicit analytic expressions to be determined for many bifurcation conditions including: the appearance of certain types of subharmonics by saddle-node bifurcations, the secondary bifurcations of these subharmonics, and global bifurcation which results in the creation of horseshoes.

MSC:
70K50 Bifurcations and instability for nonlinear problems in mechanics
PDF BibTeX XML Cite
Full Text: DOI