Welcome to the third course in the advanced spacecraft dynamics and control cruzeiro sequence. You've completed the course one and two here, where in course one, we were looking specifically at advanced spacecraft attitude control. Where we use reaction wheels, clusters of redundant wheels, or control moment gyroscopes, or even variable speed control moment gyroscopes. And how do we do three dimensional pointing? Is also dealt more deeper into basic principles of momentum, energy, and conservation, but center of mass properties of a multi body system. Then of course two, delved into the details of dynamics, where we can develop very powerful fundamental principles like Donald birth principal, Kane's equations, Lagrange's equations, and fluffy and holla gnomic constraints and all those things to develop pretty complicated equations of motion for complex systems. Now, in the capstone, we're going to touch elements from course one and two, and bring this together kind of into a fun project. So what is this project? We're going to be looking at a rigid hub simulating here as a cylinder, and then got like a solar panel, so I've got a panel that I'm attached to it, and this panel can flex. So we're modeling that through a single one degree of freedom hinges. So we're not looking at bending like Bernoulli's equation, it's still only going to have one degree of freedom for that panel. So you're also going to think of it as a deployable panel that hasn't been quite locked, and it has some stiffness, so there's two parts, two chapters of this capstone. Part one looks at the complete three dimensional cinematics of this, where you have to develop all the proper velocity, and state relationships, and validate energy expressions. But also validate using center of mass properties that you've got the right answers in this. Because what makes this interesting is that this is not rigid, so while the spacecraft hub will have a center of mass somewhere, then the panels will have a center of mass. But because the panels can move relative to the hub, both center of masses could actually move as a response, and you have to account for this. So this would be a good application of fundamental principles be covered in coarse one. And we'll get to put in some initial conditions, and make sure everything is validated the way we think it should be. But this is just for three dimensional motion the cinematics were not getting equations of motion for this. For that we go to chapter two, which will look at developing the equations of motion such that we can apply a controlled torque to the hub. Pretend you have some external torque or wheels applying this control torque to do an attitude maneuver. But now, it's doing it's subject to these panels, and if you're not careful, these will start to fly, flip back and forth, and cause all kinds of perturbations. So to get the equations of motion, we're going to be using long garages equations of motion. So you get energy is good from part one, all the energy expressions you're developing you can reduce it to a planer rotation case. And then we can use like bronzers equations in a more reasonable way to get some good answers for the equations of motion validate those. And then we can actually look at how to apply torques, and two different working strategies. In class, we talked about the importance of input shaping that you can if you're doing attitude control on structures that have flexible components. That if you don't just put in a bang bang control, which will be one case, which will excite all frequencies of the system, if you put in a smooth version of that, you might add some slight leg. But when you get there, there's only minor perturbations and reflecting on the structures versus if you just put in a bang, you will get there slightly quicker, but then takes a long time to settle. So we're actually going to numerically simulate this, which is super exciting. It's not a simple thing to do, but you have all the tools now to do this, and this should be a pretty fun project. So I hope you enjoyed, this is the last one, and after this, you have completed the advanced spacecraft dynamics and control.