Locating oscillatory orbits of the parametrically-excited pendulum
نویسندگان
چکیده
منابع مشابه
Locating Oscillatory Orbits of the Parametrically-excited Pendulum
A method is considered for locating oscillating, nonrotating solutions for the parametricallyexcited pendulum by inferring that a particular horseshoe exists in the stable and unstable manifolds of the local saddles. In particular, odd-periodic solutions are determined which are difficult to locate by alternative numerical techniques. A pseudo-Anosov braid is also located which implies the exis...
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Several new types of regular and chaotic behavior of the parametrically driven pendulum are discovered with the help of computer simulations. A simple physical explanation is suggested to the phenomenon of subharmonic resonances. The boundaries of these resonances in the parameter space and the spectral composition of corresponding stationary oscillations are determined theoretically and verifi...
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A simple qualitative physical explanation is suggested for the phenomenon of subharmonic resonances of a rigid planar pendulum whose axis is forced to oscillate with a high frequency in the vertical direction. An approximate quantitative theory based on the suggested approach is developed. The spectral composition of the subharmonic resonances is investigated quantitatively, and the boundaries ...
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For stable bipedal gait generation on the level floor, efficient restoring of mechanical energy lost by heel collision at the ground is necessary. Parametric excitation principle is one of the solutions. We dealt with the robot’s total center of mass as an inverted pendulum to consider the total dynamics of the robot. Parametrically excited walking requires the use of continuous target trajecto...
متن کاملSymbolic Computation of Secondary Bifurcations in a Parametrically Excited Simple Pendulum
A symbolic computational technique is used to study the secondary bifurcations of a parametrically excited simple pendulum as an explicit function of the periodic parameter. This is made possible by the recent development of an algorithm which approximates the fundamental solution matrix of linear time-periodic systems in terms of system parameters in symbolic form. By evaluating this matrix at...
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ژورنال
عنوان ژورنال: The Journal of the Australian Mathematical Society. Series B. Applied Mathematics
سال: 1996
ISSN: 0334-2700,1839-4078
DOI: 10.1017/s0334270000010687