Motivated by non-anthropomorphic dynamic stabilization of a walking robot, we are working on a 2D inverted pendulum stabilized with a scissored pair of control moment gyroscopes. This inverted pendulum is a fair approximation of a robot, allowing us to study the dynamics in simplified settings. In this paper we propose a model for the pendulum; the model neglects all unessential terms and thus is suitable for analysis. We also propose a simple control law based on the linearization of the model and we validate it experimentally.