00-410 Michele V. Bartuccelli, Guido Gentile , Kyriakos V. Georgiou

Lindstedt series for perturbations of isochronous systems. II. KAM theorem and stability of the upside-down pendulum (293K, Postscript) Oct 18, 00

Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

Abstract. We consider the planar pendulum with support point oscillating in the vertical direction, and we study its motion around the equilibrium point corresponding to the upside-down position. We prove that the equilibrium point is stable for the projection of the motion on the pendulum phase space (for a full measure subset of the stability region of the linearized system inside the two-dimensional space of parameters), by proving the persistence of invariant KAM tori for the two-dimensional system describing the model.

Files: 00-410.src( 00-410.keywords , bgg3.ps )