Here mi is the mass of automaton i, pij is central force acting between automata i and j, C(ij,ik) is certain coefficient associated with transferring the h parameter from pair ij to pair ik, ψ(αij,ik) is angle between directions ij and ik.
{d^2 \theta^{ij} \over dt^2} = \left( {q^{ij} \over J^i} + {q^{ji} \over J^j} \right) \tau^{ij} + \sum_{k\neq j} S(ij,ik) {q^{ik} \over J^i} \tau^{ik} + \sum_{l\neq j} S(ij,jl) {q^{jl} \over J^j} \tau^{jl} .