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Splitting-scheme Solution of the Collisionless Wigner Equation with Non-Parabolic Band Profile
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Linear stability of the spatially homogeneous equilibria of the Vlasov-Poisson system with collisions
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Asymptotic analysis of chattering oscillations for an impacting inverted pendulum
No full textThe chattering oscillations for an inverted pendulum impacting between lateral walls, a prototype
of a class of impact dampers, are analysed. Attention is focused on the periodic chattering
appearing when the rest positions cease to be attracting, and the aim is that of computing the
time τ required by the micro-oscillations to come to rest. An algorithm is proposed to compute
τ , and it is shown how this time depends on the excitation amplitude. When τ becomes equal to
the excitation period, the considered chattering is observed to lose attractivity. This occurs for a
certain excitation amplitude threshold, which is computed and whose (very weak) dependence
on the excitation frequency is illustrated.
An asymptotic estimate of the chattering time with respect to a small parameter proportional
to the excitation amplitude is given. This is obtained by an appropriate expansion in Taylor
series of the relevant quantities involved in the analysis. It is shown that τ is asymptotically
proportional to the square root of the excitation amplitude
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