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The Indian rope trick explained. (English) Zbl 0901.70017

This is not the explanation of Indian magic practices but the question of stabilizing a vertical rod, supported at its lower end, by rapidly oscillating its point of support, i.e. the inverted pendulum. One assumes that it is possible to average over the period of the forcing motion. The generalization to \(n\) jointed inverted pendula and the limit as \(n\) tends to infinity leads to a model for the rope.

MSC:

70K20 Stability for nonlinear problems in mechanics
74M05 Control, switches and devices (“smart materials”) in solid mechanics
74H55 Stability of dynamical problems in solid mechanics
93C15 Control/observation systems governed by ordinary differential equations