On the dynamic stabilization of an inverted pendulum

Abstract

A simple qualitative physical explanation is suggested for the phenomenon of dynamic stabilization of the inverted rigid planar pendulum whose pivot is constrained to oscillate with a high frequency in the vertical direction. A quantitative theory based on the suggested approach is developed. A computer program simulating the physical system supports the analytical investigation. The simulation reveals subtle details of the motion and aids the analytical study of the subject in a manner that is mutually reinforcing.

About Extracting Dynamic Information of Unknown Complex Systems by Neural Networks

“…For the real system, its equilibrium states are located on the line τ = −MLg sin θ , being saddle points the equilibrium points on −π/2 < θ < π/2, and stable focuses on the rest sited on [−π, π] [48]. Compared with the equilibrium points estimated by the NN model, it can be concluded that those points have been correctly obtained.…”

Dynamics of a Bose-Einstein condensate in a horizontally vibrating shallow optical lattice

“…[1,2] In such problems, the oscillating force, which is usually much faster than the natural evolution of the autonomous system, effectively averages to a nonzero stabilizing (or destabilizing) force. For the Bose-Einstein condensate (BEC), in the mean-field approximation, the dynamics is governed by the nonlinear Schrödinger equation (NLSE).…”

Tilted excitation implies odd periodic resonances

“…This system has attracted great attention [12][13][14][15][16][17]. It presents a wide range of dynamical behaviour, such as: the stabilization of the hilltop saddle [18][19][20][21][22][23]; the occurrence of chaotic behaviour [24][25][26][27][28][29]; the observation of period-doubling cascades [30,31] and the existence of resonance regions [11,32]. Moreover, it can be used as qualitative analogue for more complex systems [31,33,34].…”