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.

翻译：本文使用Lagrangian古典力学模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型参数模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型参数模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型的参数模型模型模型模型模型模型模型模型的参数模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型的参数模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型的参数模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型的参数模型的参数模型的参数模型模型模型模型模型模型模型模型模型模型模型模型模型的参数模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型的参数模型模型模型模型模型模型模型模型模型模型的参数模型,模型模型模型模型模型的参数模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型模型