Stabilization by vertical vibrations

SUMMARY We consider a general version of the classical problem of the stabilization of the inverted pendulum by a vertical periodic vibration of the point of suspension. Instead of the usual harmonic motion, we propose an oscillatory control with a piecewise-constant acceleration, obtaining explicit conditions over the frequency or the amplitude leading to the desired stabilization

Twist Periodic Solutions in the Relativistic Driven Harmonic Oscillator

We study the one-dimensional forced harmonic oscillator with relativistic effects. Under some conditions of the parameters, the existence of a unique stable periodic solution is proved which is of twist type. The results depend on a Twist Theorem for nonlinear Hill’s equations which is established and proved here