Periodic oscillations and attracting basins for a parametrically excited pendulum

References

• Atadan , A. S. and Huseyin , K. 1984 . An intrinsic method of harmonic analysis for non-linear oscillations . Journal of Sound and Vibration , 96 : 525 – 530 .
   Web of Science ®Google Scholar
• Blackburn , J. A , Smith , H. J. T and Nerenberg , M. A. H . 1987 . Experimental study of chaos in driven pendulum . Physica D , 26 : 385 – 395 .
   Web of Science ®Google Scholar
• Bolotin , V. V . 1964 . The Dynamic Stability of Elastic Systems , San Francisco : Holden-Day .
   Google Scholar
• Bryant , P. J . 1990 . On a periodically forced, weakly damped pendulum. Part 3:vertical forcing. Private communication 1 – 13 . to be published
   Google Scholar
• Capecchi , D . 1990 . Accurate solutions and stability criterion for periodic response of hysteretic oscillator . Meccanica , 25 : 159 – 167 .
   Google Scholar
• Capecchi , D. 1991 . Periodic solutions and stability of hysteretic oscillators . Dynamics and Stability of Systems , 6 : 89 – 106 .
   Google Scholar
• Capecchi , D. and Bishop , S. R . 1990 . Periodic and non-periodic responses of a parametrically excited pendulum , University of L'Aquila . Report 3/90. Dipartimento DISAT
   Google Scholar
• Capecchi , D. and Vestroni , F. 1990 . Periodic response of hysteretic oscillators . International Journal of Non-Linear Mechanics , 25 : 309 – 317 .
   Web of Science ®Google Scholar
• Guckenheimer , L and Holmes , P . 1983 . Nonlinear Oscillations, Dynamical Systems, and Bifurcation of Vector Fields , New York : Springer .
   Google Scholar
• Hayashi , C . 1964 . Nonlinear Oscillations in Physical Systems , New York : McGraw-Hill .
   Google Scholar
• Hsu , C. S . 1975 . Limit cycle oscillations of parametrically excited second-order non-linear system . Journal of Applied Mechanics , 42 : 176 – 182 .
   Web of Science ®Google Scholar
• Iooss , G. and Joseph , D. D . 1980 . Elementary Stability and Bifurcation Theory , New York : Springer .
   Google Scholar
• Koch , B. P and Leven , R. W . 1985 . Subharmonic and homoclinic bifurcation in parametrically forced pendulum . Physica D , 16 : 1 – 13 .
   Web of Science ®Google Scholar
• Leung , A. Y. T and Fung , T. C . 1989 . Construction of chaotic regions . Journal of Sound and Vibrations , 131 : 445 – 455 .
   Web of Science ®Google Scholar
• Leven , R. W , Pompe , B , Wilke , C and Koch , B. P . 1985 . Experiments on periodic and chaotic motion of a parametrically forced pendulum . Physica D , 16 : 371 – 384 .
   Web of Science ®Google Scholar
• Leven , R. W and Koch , B. P . 1981 . Chaotic behaviour of a parametrically excited damped pendulum . Physics Letters A , 86 : 71 – 74 .
   Web of Science ®Google Scholar
• Ling , F. H and Wu , X. X . 1987 . Fast Galerkin method and its application to determine periodic solutions of non-linear oscillators . International Journal of Non-Linear Mechanics , 22 : 89 – 98 .
   Web of Science ®Google Scholar
• McRobie , F. A . 1990 . Chaos, catastrophes and engineering . New Scientist , 126 : 41 – 46 .
   Web of Science ®Google Scholar
• Nayfeh , A. H. and Mook , D. T . 1979 . Non-Linear Oscillations , New York : Wiley .
   Google Scholar
• Parker , T. S and Chua , L. O . 1989 . Practical Numerical Algorithms for Chaotic Systems , New York : Springer .
   Google Scholar
• Rainey , R. C. T. The dynamics of tethered platforms . Meeting of the Royal Institute of Naval Architects . pp. 59 – 80. . London
   Google Scholar
• Thompson , J. M. T . Chaotic phenomena triggering the escape from a potential well . Proceedings of the Royal Society . Vol. A421 , pp. 195 – 225 . London
   Google Scholar
• Thompson , J. M. T , Bishop , S. R and Leung , L. M . 1987 . Fractal basins and chaotic bifurcation prior to escape from a potential well . Physic Letters A , 121 : 116 – 120 .
   Web of Science ®Google Scholar
• Thompson , J. M. T and Stewart , H. B . 1986 . Nonlinear Dynamics and Chaos , Chichester : Wiley .
   Google Scholar
• Tongue , H. B . 1987 . On obtaining global nonlinear system characteristic through interpolated cell mapping . Physica D , 28 : 401 – 408 .
   Web of Science ®Google Scholar
• Tso , W. K and Asmis , K. G . 1970 . Parametric excitation of a pendulum with bilinear hysteresis . Journal of Applied Mechanics , 92 : 1061 – 1068 .
   Google Scholar
• Urabe , M and Reiter , A . 1966 . Numerical computation of nonlinear forced oscillations by Galerkin's procedure . Journal of Mathematical Analysis and Applications , 14 : 107 – 140 .
   Web of Science ®Google Scholar
• Wiggins , S . 1988 . Global Bifurcation and Chaos , New York : Springer .
   Google Scholar
• Yano , S . 1987 . Parametric excitation in the self-excited vibration system with dry friction . Bulletin of JSME , 27 : 255 – 270 .
   Google Scholar