Here's a general mechanical sim that's not a rigid body, it's a multi-link system. Where I have three links, each actually has some springs on it. I'm looking at kinetic energy, actually no springs, but what I'm trying to do is, with this three-link system, is like an approximation of a flexible panel. Or this may be a multi-hinged solar panel system that was deployed, something like that. And I get my equations of motion is formed, I get my M. In this case, if you derive it, again, you don't have to be able to do this. This is just showing you the results, you can see how the M matrix depends on my states, and here are the states of the angles. What's the configuration of this multi-link system? So you can do this, and if the system is thrown out and it's jiggling and wiggling and gyrating, and you want to just make it stop, make it come to rest, all right, that's our goal. There's two different controls roll the cat. One of them is going to be basically what Tebone mentioned, minus a positive gain times the rate. And the other one I'm going to throw in is minus a positive gain times M times the rate. I call this one the momentum-like feedback. And you can see with both of these, if you plug it in here, you end up with something that's negative definite. Globally, it's asymptotic and stabilizing and all that good stuff. So both of them, if Q1 and Q2, with both controls, with the Q2, you end up with minus P2 Q transposed M(q) dot, or q dot transposed M(q) dot. That's also going to be negative definite. So both of them are globally stabilizing, just the beginning of control development. The next thing you want to look at is performance, how do they actually perform, and they're different. So, I'm throwing in a simple system to seal the simulation stuff. With control one, initially, one of them had a rate, two of them at rest. So the last link, I think, was, your Link 3, spinning, the first two was not spinning. And what happens with just a proportional control that Tebone was talking about, everything, that jiggling of the first one pulls on the second one. The second one starts to move as the second one is moving, the first one starts moving. And you can see all three links starts to move. But you're sacrificing, you're getting rid of the kinetic energy of the third link by adding some kinetic energy in the first two. And then with dissipative effect, we're guaranteed asymptotic stability, with these torques, it should settle. And it does and it converges to 0. And the control torques, you can see what happens. With the second law, where we're feeding back in angular momentum, essentially, mass times velocity is angular momentum. You get a very different behavior. You can see the third link, same initial condition, and bringing it down. But the first two links don't really budge. Any deltas you have are just due to finite control time steps that you're doing when you're implementing this. And that's because this control immediately actually applies a torque with the third link to slow it down. But it also applies a torque on the second link to keep it steady. Which, the first one, the first control didn't do. So what I'm trying to highlight here is same functions. You can derive different controls, you can prove them all, they're stable. So in your homework, you do one on a higher order spring mass system, I think it has cubic stiffness or just something like that in there. And there's actually a whole variety of controls you can come up with. And then you have to simulate it and make sure, yep, they converge, they behave as expected. Different controls, you can always argue stability, but you should also consider performance. Which performance do you like? I kind of like the second one, because if one of the links is disturbed, you can stabilize that rate without affecting or minimally affecting the other links around it. So that's kind of a nice thing.