The labeling, the numbers, right?

We tend to write, I do, certainly, I would define this as my first axis,

second axis, and third axis.

But, in fact, here I've done something that's saying is a big no,

no in this class, don't write a left-handed coordinate frame, right?

You want to write always right-handed coordinate frames.

But you could label them differently, I could go here and

say this one, I'm going to switch these and say,

okay, this one is 2 and then this one is 1,

in which case this is a correct frame, right?

So the naming of these axis is really arbitrary.

Whatever you call them, you can call them anything you wish.

Typically, we don't quite write them this way,

because this gets a little confusing, right?

Typically, what we would do is we would have a B frame.

In fact, I dropped the origin,

because in this class we're doing all attitude problems, we don't typically.

The origins you will see, we take into account when we write our positions.

We're going from here to here to here, and that's accounted for there,

the rest we don't need.

But I would typically write them this way.

[COUGH] And this has to be a right-handed frame,

so b1, b2, b3 have to be orthogonal unit length, orthogonal,

as we were talking about, and sorry, perpendicular.

But the first one crossed the second one,

has to be the third, if that doesn't match with your graphic from your

doodle that you made of the problem statement, then something's off, right?

But what we sometimes do too is maybe b2 is shared with the e frame,

and now there might be a e theta 1 axis.

And you find instead of having b2 and e theta rotating around, then always

remembering b2 is equal to e theta, you might choose to rewrite this and say,

well, this is b1, e theta, b3.

And this can be helpful too, because then we when you look at the definitions, you

quickly realize, well, the first crossed second is equal, has to be the third.

I know that e theta has to be orthogonal to b1 and b3, right?

So in the end, these frames are just names, what names do you put in?

I always suggest be lazy in this class, as a dynamicist being lazy is a big virtue.

That means you're seeking the easiest path to get from the problem statement

to the kinematic, dynamic, kinetic descriptions, all right?

And sometimes you have lots of frames,

so you really want to have simplicity, whatever makes your algebra easier.

Typically, if I have an e frame, I'm calling it e1,2,3,

and then axis are hopefully drawn to make it right-handed and work.

If I have a b frame, it's b1,2,3, if have an e frame that relates to a b frame,

I have to look at the problem statement, sometimes I keep them separate,

sometimes I put them together.

And you will see in this homework number one,

you'll be going through different problems, and

there's different ways you can solve it, but see what works well for you, okay?

But this is all just basics of coordinate frames, and vectors, and stuff.