Beginning Math and Physics for Game Programmers

Chapter 13, “Momentum and Collisions”

Axis-Aligned Vector Reflection

If the stationary boundary is vertical, v_f = [–v_ix v_iy] and if the stationary boundary is horizontal, v_f = [v_ix –v_iy] for incoming velocity v_i = [v_ix v_iy].

Non-Axis-Aligned Vector Reflection

v_f = 2 * P + v_i

where v_i = the incoming velocity and P = the projection of –v_i onto the normal of the boundary line.

Momentum

p = mv

where m = mass and v = velocity.

Impulse

Impulse = Ft

where F = net force and t = a very small amount of time.

Impulse-Momentum Theorem

Impulse = Ft = (Δp)

where F = net force, t = a very small amount of time, and p = momentum.

Conservation of Momentum Theorem

m₁v_1i + m₂v_2i = m₁v_1f + m₂v_2f

where the 1 subscript represents object 1 and the 2 subscript represents ...