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.
Reviewer: K.Horneffer (Bremen)
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 |