# Friction due to gravity in an impulse based physics engine

In my physics engine, I'm using impulses to solve collisions. I'm basing all calculations on these equations:

impulse = desired_velocity_change * mass
impulse = force * time
friction_force <= normal_force * coefficient


If an object moves along flat ground (infinite mass), after integration it'll be moving slowly "into" the ground due to gravity. This means that the impulse needed to react to that (given the restitution equals 0) will be the velocity in the direction of the contact normal, multiplied by mass.

The issue here is that gravity is a constant acceleration, which means that the object, no matter the mass, will always "dip" by the same amount given a constant frame rate. So the mass is never a factor in this situation, outside of the impulse calculation, which is just a flat velocity change.

Now, I can use impulse to calculate the force that was needed to react to the collision, this force can then be used in the friction equation as such:

friction_impulse / time <= normal_impulse * coefficient / time


Since time is always greater than 0, I can just multiply both sides by it, and then I can use the impulse equation, as such:

planar_velocity_change * mass <= velocity_change_along_normal * mass * coefficient


And again, I can just remove mass from the equation, which leaves me with:

planar_velocity_change * mass <= velocity_change_along_normal * mass * coefficient


This is the desired velocity change along the contact surface due to friction. The issue is, obviously, that none of this depends on mass, which means that no matter how heavy or light an object is, it'll always continue sliding along the surface by the same amount given a constant initial velocity.

What am I missing? It really looks like there's a logical mistake here. Should the dynamic friction depend on the mass in the first place? Moving a heavy object requires higher force, so static friction should be modeled properly, since it just flat-out removes velocity, though it'd be nice to hear if this has merit or just "looks good".

• Dynamic friction does not depend on mass. – Steve H Jan 7 '13 at 3:05
• @Steve That should be an answer. – Anko Mar 10 '13 at 14:08
• @SteveH yeah dude, if you added a reference i'd be very happy to accept that as the answer – dreta Mar 11 '13 at 7:01
• Gravity does not cause friction. – Almo May 16 '17 at 21:01