By deduction from the principle of action and reaction, if the collision impulse applied by the first body on the second body at a contact point p r ∈ ∈ R 3 is j r , the counter impulse applied by the second body on the first is − − j r . The decomposition ± ± j r = ± ± j r n ^ ^ into the impulse magnitude j r ∈ ∈ R and direction along the contact normal n ^ ^ and its negation − − n ^ ^ allows for the derivation of a formula to compute the change in linear and angular velocities of the bodies resulting from the collision impulses. In the subsequent formulas, n ^ ^ is always assumed to point away from body 1 and towards body 2 at the contact point.