1.1 Example – Double pendulum

Configuration space: \(Q=S^1\times S^1\). (Every mass moves on a circle). And note that \(S^1\times S^1\) is a torus and that the path of the end effector will be a smooth line on the torus.

One may also use points \(x_1\), \(x_2 \in \mathbb R^2\) with constraints. But, seemingly, this is more involved for discretizations.

You cannot fall off the torus, but you can violate the constraints.