Modeling of cable dynamics in cable-suspended robots traditionally focuses on implicit usage of Hamilton's principle or variational calculus to derive a PDE that governs the cable's evolution. An alternative formulation allows one to explicitly use the variational statement to directly calculate the cable's configuration update. Moreover, constraints on cables can experience numerical drift because of the indirect method by which constraints are represented in a PDE setting. Variational methods directly implement the constraint, ensuring that a constraint is satisfied for all time. Variational methods also allow the implicit treatment of constraints through generalized coordinates. In this paper, a special class of integrators known as variational integrators are used to simulate cable dynamics, including cables that have constraints, such as the catenary.