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 = ( D p )

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

Conservation of Momentum Theorem

m ₁ v _1i + m ₂ v _2i = m ₁ v _1f + m ₂ v _2f

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

Linear Collision

( v _1f “ v _2f ) = “ e ( v _1i “ v _2i )

where e = coefficient of restitution (0 < e < 1).