The space of unparametrized space curves is known to be an infinite-dimensional symplectic orbifold equipped with a canonical symplectic structure called the Marsden-Weinstein structure. But so far, no other symplectic structures have been studied on this space. I introduce more symplectic structures that generalize the Marsden-Weinstein structure. The construction is inspired by a recent trend of shape analysis. I also derive new Hamiltonian flows out of these new structures and show some computer animation of them. Based on joint work with Martin Bauer and Peter Michor.