  This paper presents an alternate form for the dynamic modelling of a
mechanical system that simulates in real life a gantry crane type, using
Euler's classical mechanics and Lagrange formalism, which allows find the
equations of motion that our model describe. Moreover, it has a basic model
design system using the SolidWorks software, based on the material and
dimensions of the model provides some physical variables necessary for
modelling. In order to verify the theoretical results obtained, a contrast was
made between solutions obtained by simulation in SimMechanics-Matlab and
Euler-Lagrange equations system, has been solved through Matlab libraries for
solving equation's systems of the type and order obtained. The force is
determined, but not as exerted by the spring, as this will be the control
variable. The objective to bring the mass of the pendulum from one point to
another with a specified distance without the oscillation from it, so that, the
answer is overdamped. This article includes an analysis of PID control in which
the equations of motion of Euler-Lagrange are rewritten in the state space,
once there, they were implemented in Simulink to get the natural response of
the system to a step input in F and then draw the desired trajectories.
