AA << present results of linear and nonlinear motions of a parametrically driven coplanar double pendulum with velocity-dependent damping. The equations of motion of a damped double pendulum of unequal masses with its pivot vibrated vertically are different from those obtained under gravity modulation.
Linear stability analysis shows that tongue-shaped marginal stability curves divide the plane of driving parameters into multiple regions of subharmonic and harmonic instabilities. The instability zones for one normal mode overlap with those for the other.
The double pendulum may oscillate or rotate about its pivot harmonically or subharmonically. The limit cycles corresponding to the normal mode oscillations of a double pendulum of equal masses are squeezed into a line in its configuration space.
For unequal masses, two marginal curves for subharmonic instabilities merge to form a double-well shaped curve in the presence of damping, which is qualitatively new. The pendulum shows driving amplitude sensitive multi-period complex oscillations for driving parameters near the extrema of the merged instability zones and boundaries of the overlapping zones.
For larger driving amplitude, the pendulum shows subharmonic, harmonic or chaotic rotations. >>
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Rebeka Sarkar, Krishna Kumar, Sugata Pratik Khastgir. Parametrically driven damped coplanar double pendulum. arXiv:2208.03292v1 [physics.class-ph]. Aug 2, 2022.
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keyword 'pendulum' in FonT
keyword 'pendolo' | 'pendola' in Notes
(quasi-stochastic poetry)
Keywords: gst, pendulum, double pendulum, instability, chaos, chaotic rotations
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