We recall the question of geometric integrators in the context of Poisson geometry, and explain their construction. These Poisson integrators are tested in some mechanical examples. Their properties are illustrated numerically and they are compared to traditional methods.

翻译：我们回顾了泊松几何背景下几何积分器的问题，并解释了它们的构建方法。这些泊松积分器在一些力学实例中进行了测试。通过数值计算展示了它们的性质，并与传统方法进行了比较。