Or you could imagine, the right coordinate system.

And we've also seen that we could change our coordinates.

So let's remind ourselves what a coordinate system is here.

The coordinate system is defined based on the robot, where it is and what it's looking at.

If you want to represent v2 in your new basis, well, what is it?

So our new coordinate system has the basis vectors v1 and v2.

So if I multiply D times the second basis vector v2 in B coordinates, in our new coordinate system, that is equal to d1, d2 times what is this guy's representation in our new coordinate system?

I'm claiming that the coordinate system, with respect to this, is good. But what does it mean to be good?

Dispatches!

The dispatches...

The equatorial coordinate system is a widely used celestial coordinate system used to specify the positions of celestial objects.

So if we're dealing with Rn So the standard basis for Rn is equal to Well, I could write it as e1, e2, and all of that, but I'll actually write out the vectors.

Some coordinates.

And now in this world, our transformation is just a reflection around our new vertical axis.

The computations for many problems get a lot simpler if you pick the right coordinate system.

So there's a difference in their x's squared plus a difference in their y's.

Batteries One and Two commence firing... on coordinates 325878.

This is, of course, the Cartesian coordinates.

So what are these coordinates?

This is in standard coordinates.

So that vector, or the position specified by the vector, 8, 7, could just as easily be specified in our new coordinate system by the coordinates 3, 2.

They are obtained from the applied forces, Fi, i 1..., n, acting on a system that has its configuration defined in terms of generalized coordinates.

The center of the bank is at .

We don't have a working system here yet.

My partner sees the target, tell me the coordinates and distance

And then the coordinate tells me how many v1's do I have. So

So these are coordinates with respect to b.

So when you represented 2, 1 in your new basis with respect to this, of course, it's 1 times this plus 0 times this. It's going to be 1, 0.

quot (i) To strengthen the functioning of the resident coordinator system

The one physical system, the brain, contains an accurate working model of the other the quasar.

That point has the co ordinates, tells me where do I find that point ( 2, 5). and these coordinates are called 'cartesian coordinates' named for René Descartes because he is the guy who came up with these.

The coordinates are just going to be, the coefficients on the different basis vectors.

Let's see, when you go from the distance squared, the difference is in there x's.

Let me draw three coordinate axes. So that's my first x axis and y axis, so x and y.

All right, let's keep converting Cartesian functions to polar coordinates.

So literally is the B coordinate representation of the transformation of x.

So if we want to go from x to the B coordinates of x, I take my x and I multiply it times C inverse. C inverse is this thing right here.

To do so, the function must be adapted to the new coordinates.

The origin, ( S , M , L ) (0,0,0), corresponds to black.

Here is the invitation, giving the exact coordinates in time and space.

You're definitely the first. Okay, first coordinate. One two three nine.

And that spider web pattern corresponds to the local coordinates in the sky.

We've been talking about alternate coordinate systems, and this transformation, it looks difficult in our standard coordinate system, because we're reflecting around this line right there.

This may make defining the vectors simpler when writing the equations of motion.

Different coordinate systems are just different ways of representing the same vector.