A simulator for simulating a first object and a second object that is coupled to the first object is disclosed. The simulator models the first and second objects as a plurality of segments, with each segment having a plurality of nodes connected by one or more edges. The simulator then indexes each of the nodes and couples at least one node of the first object to a node of the second object. The indexing and coupling is based on the current simulated position of the first and second objects. The simulator then generates and solves a linear system of equations Ay=b from the indexing, and updates a position of each of the nodes. The simulator flow then dynamically re-indexes the nodes, and continues in a loop.