We consider the following dynamical system: two rigid bodies are freely moving on a plane, with the only constraint that they are connected at a point about which they can rotate. There is no gtravity and no friction (like two rigid bodies moving on ice). The motion can be described in a phase spece of dimension 6 (three position parameters and three momenum parameters), but there are several conserved quantities. The goal of the thesis to describe the system mathematically and to obtain an overview on the possible orbits.