Bishop, S. R.; Clifford, M. J. Non rotating periodic orbits in the parametrically excited pendulum. (English) Zbl 0809.70015 Eur. J. Mech., A 13, No. 4, 581-587 (1994). Summary: Non-rotating solutions for the parametrically excited pendulum are considered, and comparison is made between the pendulum and a system which permits escape from a symmetric potential well. Two escape or failure scenarios are identified by a bifurcation diagram, and stable periodic orbits are identified using methods of symbolic dynamics and path following techniques. Cited in 5 Documents MSC: 70K28 Parametric resonances for nonlinear problems in mechanics 37G99 Local and nonlocal bifurcation theory for dynamical systems 37E99 Low-dimensional dynamical systems Keywords:escape; symmetric potential well; failure scenarios; bifurcation diagram; methods of symbolic dynamics; path following techniques PDFBibTeX XMLCite \textit{S. R. Bishop} and \textit{M. J. Clifford}, Eur. J. Mech., A 13, No. 4, 581--587 (1994; Zbl 0809.70015)