Multipulse orbits in the motion of flexible spinning discs

N Malhotra, N Sri Namachchivaya… - Journal of Nonlinear …, 2002 - Springer
N Malhotra, N Sri Namachchivaya, RJ McDonald
Journal of Nonlinear Science, 2002Springer
The global dynamics of flexible spinning discs are studied. The discs studied are
parametrically excited in their spin rate, and have imperfections that cause symmetry-
breaking. After determining the equations of motion in a suitable form, the energy-phase
method is employed to show the existence of chaotic dynamics by identifying multipulse
jumping orbits in the perturbed phase space. We provide restrictions on the damping,
forcing, and symmetry-breaking parameters in order for these complicated dynamics to …
Summary
The global dynamics of flexible spinning discs are studied. The discs studied are parametrically excited in their spin rate, and have imperfections that cause symmetry-breaking. After determining the equations of motion in a suitable form, the energy-phase method is employed to show the existence of chaotic dynamics by identifying multipulse jumping orbits in the perturbed phase space. We provide restrictions on the damping, forcing, and symmetry-breaking parameters in order for these complicated dynamics to occur. The dissipative version of the energy-phase method predicts a wider range of values for which chaotic dynamics occurs than the traditional Melnikov method. The results are then discussed in terms of the physical motion of the spinning disc system. The multipulse orbits are manifested in the physical system as a shifting between two different nodal configurations of the disc. When the motion is chaotic, an observer will see a random jumping between the two nodal configurations of the disc.
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