- 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
Oct 18, 00
(auto. generated ps),
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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.