Equations (6a), (6b), (7) and (8) describe the Coulomb friction model in terms of forces. By adapting the argument for instantaneous impulses, an impulse-based version of the Coulomb friction model may be derived, relating a frictional impulse j f ∈ ∈ R 3 , acting along the tangent t ^ ^ , to the reaction impulse j r ∈ ∈ R 3 . Integrating (6a) and (6b) over the collision time interval [ t 0 . . t 1 ] yields