Abstract: A significant challenge in applications of computer animation is the simulation of ropes, cables, and other highly constrained strandlike physical curves. Such scenarios occur frequently, for instance, when a strand wraps around rigid bodies or passes through narrow sheaths. Purely Lagrangian methods designed for less constrained applications such as hair simulation suffer from difficulties in these important cases. To overcome this, we introduce a new framework that combines Lagrangian and Eulerian approaches. The two key contributions are the reduced node, whose degrees of freedom precisely match the constraint, and the Eulerian node, which allows constraint handling that is independent of the initial discretization of the strand. The resulting system generates robust, efficient, and accurate simulations of massively constrained systems of rigid bodies and strands.