Resolved J impulse is wrong

Hello folks!
I noticed that "Impulse applying equation" is incorrect in all Physics Engines and papers

Specially, applying Linier Impulse is incorrect. here the equation :

va2 = va1 + j n / ma
ωa2 = ωa1 + (rap × j n) / Ia




In the Equation above, Linear impulse never considering contact point location, e.g if its close to Center of Mass. And this is completely incorrect. Since force or impulse Vector should be divided with Vector separation rules.

Meanwhile, this equation shows its main incorrect value when an impulse or force vector perpendicular to the collision arm vector. Indeed in this case, Linear Impulse should be zero. but the equation above adds additional impulse to the Linear velocity




Here I proposed my own fixed equation for applying Impulse or Force for a Rigidbody


va2 = va1 + (rap · j n) / ma ----(Dot product of "collision normal" and "collision arm")
ωa2 = ωa1 + (rap × j n) / Ia







Please, let me know what do you think about my proposal ! Because Impulse applying formula is core of the Physics Engine, the incorrect formula totally changes realism of the simulation.

 

I think this is a very broad assumption. Couldn't be just you?

Ok, here is the problem. Everything you describe is wrong. But it's ok, I also experienced the same confusion as you (and thought the same) the first time I faced these situations. I know that understanding this is not intuitive, but there's an explanation for the actual impulse equations not to consider the contact point location.

Please check out the section 5.5 " Force vs. Torque Puzzle" of this paper. The case is nicely explained there:
https://www.cs.cmu.edu/~baraff/sigcourse/notesd1.pdf

Here are the relevant figures:

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As you can see, the velocity (impulse) is the same regardless the contact point. Surprisingly, that's how it works in real world physics.

That would mean that any force applied in a direction that forms an angle of 90 degrees with the vector of the contact point wrt the center of mass would apply 0 impulse, even if the contact point is just 1 mm away of the center of mass, no matter the magnitude of the force. It's evidently incorrect.

 

Hello! @Edy


1) Here, still, what I believe is that Linear Force value should be changed into vector projection when its away from Center of Mass (COM).

Since it shows huge inaccuracy when force or impulse far away from COM.



2)As, it was mentioned in the paper, E kinetic energy depends on path that travel during the force applied.
But what if there is an "Impulse" instead of a "Force". Why the applied impulse should gain more impulse than its original value.





Yet, this collision formula is in the field " Algebraic Collision Law", which means ,no matter what , the final result is not going to give 100% accurate result because of few computation.

Nevertheless, I still believe linear impulse or force vector should be given by its projected vector value to the Rigidbody, even "Algebraic Collision Law" used to solve collision response or applied energy.

 

That would lead to incorrect and unrealistic results. Believe it or not, physics in reality work as described and formulated in the papers.

An impulse is a force applied during a very short amount of time. Result is the same.

The applied impulse (== force) does more work when applied off-center, so it gives more kinetic energy to the rigid body: same kinetic energy as per the same velocity and additional kinetic energy as per the added angular velocity.

Again, I know it's difficult to understand. And again, that's how physics work in reality, believe it or not. The problem is not the physics or the papers, but understanding a correct concept that seems not intuitive at first.

Think on the billiard/pool players when they hit the ball off-center. The ball receives the same velocity as when hit in the center, but the off-center distance also gives them additional angular velocity.

 

Finally I've just figured out that this formula is correct and proved with a simple lever example