I keep reading that the configuration space of a given system is the "space of all it's posible positions". Along with this is the inevitable example that the configuration space of a double pendulum is the 2-torus, S^1 x S^1. This makes sense: the possible positions of the first bob is a circle around the "fixed point" , while the possible positions of the second bob is a circle around the first bob. So it is clear how one may identify all the possible positions of the system with the points of S^1 x S^1. Additionally, the motion of the system in time is clearly a continuous path on S^1 x S^1 with the its usual (product) topology. So as I said, this is all intuitively clear to me. But when I try to find a formal definition of configuration space in order to make the above reasoning rigourous, I fail. So, does anyone know the formal definition of configuration space?? Thanks!