In this paper, we report a recursive inverse dynamical model for a new snake-like robot called NATRIX. This robot has been designed to maintain its gaze on the water surface and monitor sensible ecosystems. Inspired by real snakes, the robot features rotating outer shells allowing to change the level of immersion of each module and re-stabilize quickly the robot. This new degree of freedom leads to an original treelike geometric structure. We present here the theoretical model and the numerical solutions that allow us to simulate in real time the dynamics of the robot on the water surface. After reporting the benchmark of the simulator, we present surprising preliminary results suggesting the possibility of capsizing for a given frequency range.