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  • 1
    Electronic Resource
    Electronic Resource
    The dynamics of a bouncing ball with a sinusoidally vibrating table revisited (1996)
    Springer
    Nonlinear dynamics 10 (1996), S. 1-18 
    Details
    ISSN: 1573-269X
    Keywords: Bouncing ball ; vibrating table ; stability and bifurcation ; period-1 motion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The dynamical behavior of a bouncing ball with a sinusoidally vibrating table is revisited in this paper. Based on the equation of motion of the ball, the mapping for period-1 motion is constructured and thereby allowing the stability and bifurcation conditions to be determined. Comparison with Holmes's solution [1] shows that our range of stable motion is wider, and through numerical simulations, our stability result is observed to be more accurate. The Poincaré mapping sections of the unstable period-1 motion indicate the existence of identical Smale horseshoe structures and fractals. For a better understanding of the stable and chaotic motions, plots of the physical motion of the bouncing ball superimposed on the vibration of the table are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00114795
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Resonant-Separatrix Webs in Stochastic Layers of the Twin-Well Duffing Oscillator (1999)
    Springer
    Nonlinear dynamics 19 (1999), S. 37-48 
    Details
    ISSN: 1573-269X
    Keywords: resonant-separatrix web ; stochastic layer ; energy spectrum ; Duffing oscillator
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The excitation strength for the onset of a new resonant-separatrix in the stochastic layer of the Duffing oscillator is predicted through the energy change in minimum and maximum energy spectra. The widths of stochastic layers are estimated through the use of the maximum and minimum energy which can be measured experimentally. The energy spectrum approach, rather than the Poincaré mapping section method, is applied to detect the resonant-separatrix web in the stochastic layer, and it is applicable for the onset of resonant layers in nonlinear dynamic systems. The analytical condition for the onset of a new resonant-separatrix in the stochastic layer is also presented. The analytical and numerical predictions are in good agreement.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008383030507
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    Paper (German National Licenses)
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