Efficient factorization inertia matrix for branched interconnection structure of multibody system

The article describes the factorization algorithm that exploit branch-induced sparsity in the inertia matrix of multibody system with tree interconnection structure. It also presents formulas that show how the cost of factorizing the inertia matrix vary with the topology of the tree. These formulas show that the cost of calculating forward dynamics for a branched tree can be considerably less than the cost for an unbranched tree of the same size. Presented some examples of kinematic trees for which the complexity of factorizing the inertia matrix are less than O(n3).