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A mechanical model of a balancing system is constructed and its stability
analysis is presented. This model considers an interesting practical problem,
the backlash. It appears in the system as a nonlinear spring characteristic
with noncontinuous derivative. The upper equilibrium of the pendulum can
be stabilized without backlash. Backlash causes oscillations around this equi-
librium. Phase space diagrams are revealed based on simulations. Bifurca-
tion analysis is carried out by the continuation method. The noncontinuous
derivative of the spring characteristic causes problems during the calcula-
tion, therefore different types of approximate characteristics are used. The
conditions of the existence of stable stationary and periodic solutions are
determined in case of the approximate systems and conclusions are obtained
for the exact piecewise linear system.
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