Beginning Math and Physics for Game Programmers

Modeling Collisions

The last section took a one-sided approach by looking at the effects of a collision on just one object using the impulse-momentum theorem. Now let's look at the effects on both objects involved in the collision. If two objects collide, and both can move, they both apply an impulse to each other due to the collision. Let's look at the impulse-momentum theorem one more time:

Ft = (Δp)

Let's divide both sides by time:

F = (Δp)/t

Newton's Third Law states that for every action there's an equal and opposite reaction. In this case, one object places a force on another object, and at the same time, the second object places an equal and opposite force on the first object:

F₁ = –F₂

Now let's substitute the impulse-momentum theorem ...