STABILITY AND BIFURCATION BEHAVIOR OF AN INVERTED PENDULUM WITH FOLLOWER FORCE

Svetoslav Nikolov; Valentin Nedev

Scientific paper ID 775 : 2013/2

STABILITY AND BIFURCATION BEHAVIOR OF AN INVERTED PENDULUM WITH FOLLOWER FORCE

Svetoslav Nikolov1,2, Valentin Nedev2

The study of dynamics of an inverted pendulum with follower force is of interest to several fields of physics, mechanics and engineering. Using Lyapunov-Andronov’s theory, we find a new analytical formula for first Lyapunov value at the boundary of stability. It enables one to study in details the bifurcation behavior of dynamic systems of the above type. We check the validity of our analytical results on the first Lypunov’s value by numerical simulations. Our numerical analysis suggests that follower force have stabilization dynamical role and hard stability loss take place.

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обърнато махало проследяваща сила устойчивост бифуркационно поведениеinverted pendulum follower force stability bifurcation behaviorSvetoslav Nikolov Valentin Nedev

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