1. Reference problem

1.1. Geometry

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

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

1.2. Material properties

Pendulum linear mass: \(1.\mathrm{kg}/m\)

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

1.3. Boundary conditions and loads

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

1.4. Initial conditions

The pendulum is released without speed from horizontal position \(\mathrm{OP}\).

\(\theta =+\frac{\pi }{2}\), \(\dot{\theta }=0\)