This still belongs to the category of

kinetics in the sense that we're trying to find equations of motion.

We have found equations of motion and you started that with blobs,

let me frozen so we have a nice rigid body.

Then we found them for a single rigid body, studied equilibrium, stability,

all the uncontrolled things.

Then we had systems of rigid bodies where we had maybe a dual spinner, so

it was a craft in one wheel.

Now we're going to go a little bit crazy here, not just do craft in one wheel but

craft in n wheels.

And not just body fixed wheels but even ones that can spin and

twist relative to the body.

Those things are called controlled mono gyroscopes.

So with all these extra things there's benefits but also challenges.

The mathematics gets a lot more complex.

So in your last homework actually you derived these in via CNG equations,

the path is all in the book.

We're covering everything in class, so

as we go through these I'm going to show you some highlights.

Maybe go through some of these equations.

Show you how you can get from this step to this step.

But I'm not going to do every single mathematical detail.

You do that actually at the end when you put it back yourself in the homework.

But then you see all the sub steps.

You can see yep this is what I should be getting.

Great I'm on track.

If you're stuck with a sub step you can use the next sub step and move on, right?

And then come back to that one later if you have to.

So everything's there.

So the way I'm teaching this is more of a overview.

We want to cover the topics and concepts and how this comes together.

So we'll talk about momentum control devices.

There's some pictures and just conceptually why do people like this?

It's kind of an icing.

And then we can get into the math equations of motion and

we're going to derive it in the most general way.

There's something called verbal speed control moment gyroscope.

Typically there's just CMG's within a single axis or dual axis,

double gamble CNG devices.

But there are also some that have been researched that have been variable speed

and you'll see the benefits.

If we do a variable speed control moment job scope upfront

we're doing the most complex version.

And then at the end we can go well, what if it is just a reaction mill?

What if it is a CMG?

So we can free certain modes in the mathematics and certain terms go to zero.

And you regain the classic reactional solution or CMG solution or the hybrid,

right?

So instead of doing this two, three times, we'll do it once in the most general and

then specialize.

That's the approach that we're doing.

So we'll go through a single VSCMG first, talk about the motor torque calculations.

Clusters often too, that's we have multiple devices.

Basically comes to summation,

once you know how to do one doing the others is kind of a ditto.

It's more of a bookkeeping step so it doesn't take long to do that.