Reference problem
=====================


Geometry
---------


.. image:: images/100005F4000014770000130422CBDAA539531E59.svg
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    :height: 245


.. _RefImage_100005F4000014770000130422CBDAA539531E59.svg:

A rigid :math:`\mathit{OP}` pendulum with a length of 1 and a center of gravity :math:`G` oscillates around the point :math:`O`.

The angular position of the pendulum is indicated by: :math:`\alpha \mathrm{=}\theta \mathrm{-}\pi`


Material properties
-----------------------

Pendulum linear mass: :math:`1.\mathrm{kg}/m`

Axial stiffness (product of Young's modulus by the area of the straight section): :math:`{1.10}^{8}N`


Boundary conditions and loads
-------------------------------------

The pendulum is articulated at the fixed point :math:`O`. Under the action of gravity, its :math:`P` end oscillates on the semi-circle :math:`(\Gamma )` with center :math:`O` and radius :math:`1`. There is no friction.


Initial conditions
--------------------

The pendulum is released without speed from horizontal position :math:`\mathrm{OP}`.

:math:`\theta =+\frac{\pi }{2}`, :math:`\dot{\theta }=0`