  In this paper, is used the Lagrangian classical mechanics for modeling the
dynamics of an underactuated system, specifically a rotary inverted pendulum
that will have two equations of motion. A basic design of the system is
proposed in SOLIDWORKS 3D CAD software, which based on the material and
dimensions of the model provides some physical variables necessary for
modeling. In order to verify the results obtained, a comparison the CAD model
simulated in the environment SimMechanics of MATLAB software with the
mathematical model who was consisting of Euler Lagrange's equations implemented
in Simulink MATLAB, solved with the ODE23tb method, included in the MATLAB
libraries for the solution of systems of equations of the type and order
obtained. This article also has a topological analysis of pendulum trajectories
through a phase space diagram, which allows the identification of stable and
unstable regions of the system.
