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Remarks on stability of inverted pendula. (English) Zbl 1150.34021
The paper considers stabilization of the unstable equilibrium of the double inverted pendulum under a parametric fast oscillation. The paper displays new results on monodromy matrix computation via a series expansion and stability of the first order averaging. Both planar and spherical pendula are considered.

MSC:
34D20 Stability of solutions to ordinary differential equations
34H05 Control problems involving ordinary differential equations
34C29 Averaging method for ordinary differential equations
34E20 Singular perturbations, turning point theory, WKB methods for ordinary differential equations
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