About the book
In the field of analysis, inverted pendulums are characterized by being continuous systems
subjected to the action of axial compression forces. When slender, these elements can reach
an ultimate limit state defined by the loss of their stability, without having yet exhausted the
resistant capacity of their sections. For these systems, the analyzes performed to evaluate the
loss of stability by equilibrium bifurcation should consider both the effects of the existing
distributed and concentrated normal force, as well as the peculiarities of the materials of
which they are constituted, their behavior regarding elasticity, viscoelasticity or even plasticity,
as well as deterioration factors. In this regard, all changes to the material over the life of the
system must be considered. It is important to remember that column buckling was initially
studied in the field of static, in rational mechanics. However, this is essentially a dynamic
phenomenon whose solution is based on stiffness and mass. Whether by static or dynamic
path, analyzes of inverted pendulum need to be done by observing the total stiffness of the
system, which must be composed of all terms of interest. In addition to considerations of loss
of equilibrium, in dynamic analysis it is still possible to obtain frequencies and modes of
vibration, essential characteristics of these systems. In relation to the dynamic aspects,
inverted pendulum is a class of systems widely used as control strategies.